It's been a few years since I did the same thing to my '85 engine. fire$tone tire creatures did a preventative check on the truck and cross threaded my #1 spark plug.
I have the '85 FSM for the 22r/e engine. It does not state anything about positioning the engine/cylinders prior to installing the head.
Here are the readers digest version of the steps.
1. apply sealer to the cylendar block
2. install cylinder head
(a) align the alignment marks placed on sprocket and chain during removal
(b) position cylinder head over dowels on block
3. install rocker are assembly
(a) place rocker assembly over dowels on head
(b) install and tighten head bolts (three passes) 58 ft-lb.
4. install chain cover bolt (9 ft-lb)
5. install cam sprocket on cam shaft
(a) turn cam to position alignment dowel at the top
(b) while holding cam sprocket and chain, turn crank until #1 and #4 cylinders are at TDC
(c) place sprocket over end of cam dowel
6. install dizzy .....
From step 5 it sounds as thought the pistons aren't supposed to hit the valves.
What if you backed off the head bolts to release the tension on the rocker assembly? This wild release all the valves and allow you to position the crank.
And then rotate the cam to TDC before re-tightening the head bolts.
HTH