Total kill and reseeding. Lawn was sprayed with gly 2 weeks prior.
^ this is a key factor that you did a complete re-do, otherwise I would suggest to only TINE (not flail) dethatch it because a spring/tine gives great results to thicken up an already-decent lawn without damaging existing grass.
I would not run a slice seeder over a decent lawn, only a tine thatcher and then an aerator. Bagging the thatch in between (it's usually not even thatch unless it's Kentucky blue or zoysia for cool season grasses, tall Fescue doesn't actually create thatch but it does get a base layer of brown dead grass that will block seed-to-soil contact.
A slice seeder can damage crowns of good existing grass. Yes new grass will grow in place of it but it's better to have established mature grass with deep roots than young fragile grass. As you know, the slicer should basically only scratch the surface at 1/4" for optimal seeding depth but almost no lawn is a pool table, so even if the slicer is only set to 1/4" , you'll hit high spots that basically become tilled and beats up the existing good grass.
But as mentioned, this was a spray it all dead and re-do, so to answer your titled question, I would slice first. This way the slicer cuts through the woody dead crowns of the old weeds so that the new seed can more easily root down to actual soil. Why the machine is clogging I dunno.
Rolling in seed is almost a magic trick. Great improvement in germination. Topdressing afterward would tend to help keep things moist but it's a lot of work.
I basically only use a roller after tilling. Because it'll be a soft muddy mess if not.
Tilling is great because it does aeration and seed-to-soil contact all at once, and can often give great results on weedy lawns without using any chemicals.
I mean, optimally you would till and then roll, then water and wait for weeds, then spray a few weeks later any weeds that pop up, and then finally seed. But you can till a weedy lawn if you shred it up finely and a lot of new grass will grow to choke out previous weeds from popping back up. Annual weeds such as crabgrass and foxtail though have no need to spray dead - just scalp bag then till it finely and seed heavy in Fall when grassy weeds aren't germinating.
The problem with tilling though is re-grading perfectly can be a PITA.
Rolling in seed is almost a magic trick. Great improvement in germination. Topdressing afterward would tend to help keep things moist but it's a lot of work.
Topdressing not only holds moisture but more importantly gives top and bottom seed-to-soil contact. But there's usually no need to bring in more soil especially if you aerated too - watering will melt the cores and everything together to coat the seeds with dirt. That's if it were tine thatched also.
Watering also melts slit seeder cuts to fold seeds inside slits like a lawn roller would. But rolling does hide seeds from birds more quickly but I put the 'thatch' back over the seeds anyway, or lightly rake it all together.
I'm told on here that native soil is usually perfectly fine, and I have to agree from what I've seen as long as it's not obviously too sandy or clay-like. Compost basically brings in a lot of organic nutrients which are great but so does milorganite if soil test shows a deficiency or pH needs that's a different story.
But if soil is very sandy or clay-like, then yes, till in new compost/topsoil, or at least core aerate and then topdress so the compost gets down in the holes to make soil composition more optimal instead of just topdressing new soil/compost on top of a sandy/clay native soil. Tall Fescue can root about 2.5 feet, it usually doesn't but should still till everything together to make the deeper soil solved from being too sandy/clay.
Been trying a few different approaches to overseeding this year to reduce non-mechanized labor but still getting good results. Latest "experiment" was aerate, spread seed and then mow lawn to cover it with the grass clippings. The seed didn't get blown around much so the mowing didn't seem to hurt things in that regard. I'll see how it worked out in a few weeks.
oof, I'm very hesitant to do that. My reasoning is that fresh cut green grass needs to decompose. And I don't want that happening right on top of tiny seedlings. It can potentially compost the little seedlings to death. That's another reason why I bag the first few cuts after seeding, a rare instance that I suggest bagging (as well as scalp bagging before seeding too). Bag the first few cuts to prevent that potential composting effect and also to not cover the new seedlings with clippings which need sunlight.
When I use the tine dethatcher, I put that thatch back on top as the final step but it's already brown and dead (like straw). This holds in moisture and hides seeds from birds, and somewhat holds seeds in place on a slope, and makes use of all that thatch. I just wish they made a mini hand held straw shredder blower that I can load with the thatch and broadcast it in a thin even layer instead of spreading it by hand.
IMO there's no sense in killing and reseedIng a lawn that is failing due to poor soil....if you're not going to also take steps to improve the soil.
If you dig down and see it's obviously sandy, then it won't have drought resistance , so yes I would suggest tilling in tons of compost/soil but I think it's rare that the top foot or two of a yard is overly clay like or sandy. At least around here. I know some parts of the country are extremely clay-like but usually soils are loamy and good for grass.
Sorry if I wrote way too much info but I tend to just write it all out while I'm at it, also in case it helps anyone else.
So basically if lawn is already decent: In late summer/early Fall: scalp bag on lowest height, tine dethatch, bag the 'thatch' (usually not actually thatch because fescue is probably the most common grass), then core aerate, spread seed, put a thin layer of thatch back over, then fertilizer, then watering schedule. Never fails. I've put that 'thatch' back over somewhat heavy too like 1.5" but Tall fescue grows right through it. If run the thatch over on the side walk or something and bag it, it will make it more powdery and much easier to spread evenly by hand.
If it's all weeds, there's more options, and I'm not sure which is best and easiest but all options work. (It's pretty easy to get a good stand of grass to germinate in Fall, the trickier part I think is maintaining it long-term with proper selective weed control and follow up reseeding, frequent mowing to promote denser turf, high 4" tall fescue mowing to prevent weeds and to help with drought resistance, watering regularly at least for the next year to develop deep roots and then tall fescue should be ok to not even water anymore except for serious drought in summer).
If all weeds:
Call till it all finely without chemicals and get decent results (good soil contact and full soil aeration) but need to re-grade and roll the yard.
Can spray it all dead before (or not), then scalp mow and then use a FLAIL dethatcher slow and deep to rip up the woody crowns of all the dead weeds and then remove that debris and will have a pure dirt seed bed. Can then roll the seeds to hide it from birds and/or put straw over it which will also hold seeds in place.
Spray it all dead (or not) and scalp mow and then just core aerate the F out of it like 10 passes will give a great seed bed. Can put some seed down before the last few passes with the aerator then more seeds on top and then watering will melt it all together. Can put straw over also to hold seed in place and hide from birds and hold moisture.