I am getting ready to do our final round in the next week or so. Cool season fescue, will apply whatever I put down at 1lb N/1000. Question is will 34-0-0 ammonium nitrate be a bad idea/or could it damage new grass that was installed via overseed approx. 5-6 weeks ago.
Lowe's locally has this stuff on clearance
I might suggest that you double-check the label on the product. Not many retail stores carry ammonium nitrate because of the storage and reporting limits placed on it by various government agencies. My guess is that it would be a urea product. Just because its a 33-0-0 or 34-0-0 product doesn't mean that it's necessarily ammonium nitrate.
Even if you did find ammonium nitrate to apply, go for it. It's not a bad fertilizer at all. It can burn turf when applied at higher rates, especially young seedlings, so the rate you use is going to be important, as is you ability to water in the application.
If it were my lawn and I were using ammonium nitrate, I would apply no more than 0.5#N/M and water it in right after with at least 0.25" of water. If you can't water it in right after, then wait until you have some rain in the forecast and apply right before the rain (assuming you're not expecting a downpour).
Some other posters suggested using something with P in it -- that's a great idea. Those little seedlings have short roots and can't access as much P as established plants can. Applying some P will help those young plants get started before the winter.