I may be misunderstanding your situation. Here goes: From your tank (female thread) install a reducer (male Threaded 1" to a barbed 3/4") attach your hose 3/4" to your roller pump with another barbed to 3/4" male thread. From the pump with another 3/4" threaded male to a 3/4" barbed fitting to your manifold. All 3/4" plumbing. I like these rather than a T fitting because you can mount it and then go to your by-pass regulator or any other type. On another stem from you can have your line to your reel. Manifolds let you adapt any number of fitting or another for a clean-out. Rather simple install. With the regulator on one of the manifold stems it will let you regulate the pressure as it goes to your reel. I have my gauge on the manifold and another at the boom end with a regulator to maintain even pressure. Rittenhouse has these. Give it some thought. Your tee will work but does not give you the advantages to adding. You can get brass reducers from 1" to 3/4" with male threads and female on the inside. From there it should be a piece of cake. Make sure that you use nylon take as your pump is cast iron and brass fitting are dis-similar metals and could gauld. Another reason to use nylon fittings instead of brass.
We all are merely gleaners from the masters who were here before us.