Using a shortened range of motion should be a technique used deliberately and for a specific purpose, not the accidental result of going too heavy. Like TX and Furius said, your goal will play an obvious role in what/how you should lift, but the big thing is to be aware of when/if/why/how you'd use an abbreviated ROM.
If you have a chronic shoulder issue that keeps recurring, even though you said it was a year ago and you're "fully rehabbed", I'd suggest working the shoulder with a full ROM on presses. Especially alternating DB presses like you're doing, which are a great unilateral exercise that bring in all sorts of shoulder stabilizers, you get more overall benefit to training the shoulder joint through its complete ROM.
If you want to use a shorter ROM (intentionally and for a specific purpose), use it with laterals (lots of guys are fans of John Meadows' advice on those) or with barbell/"regular" 2-DB/machine presses, not 1-arm presses.