If there is a chance of having an absess .... please get it taken care of asap! A bad tooth can create a lot of problems - and a lot of expenses. If you can wait til May, I understand the economics very well. It may be worth waiting if you feel you can deal with all the 11 or 12 teeth out at the same time - or close to it.
Long ago, I had partials on the top and bottom. Then, it became necessary for me to have major work - so the balance of the top + a couple from the bottom were removed .... a total of 14-teeth all at one sitting. It was good to have it all over with at one time ... for a plate on top and a slightly larger partial on the bottom.
It is a very personal decison to make - just don't let an absess happen or go without attention.
I too have had sinus problems for a long time with major surgery on the sinuses 15-years ago .... so I can appreciate the added problem.
Rob & Gizmo