There are various ways of re-engineering, or re-making, the cover to need less clearance above the drill for it to open. Best to make a prototype or mock up before operating on yours tho'. I'd probably make from scratch, especially as I feel that a simple front pulley shield is fine in a personal workshop.
1) Arrange things so it slides off forwards rather than hinges up. Will need to operate on the back so it clears the motor pulley and arrange some sort of rail or rod for it to slide on which doesn't sound intrinsically impossible. Hafta remember to move the quill down a bit when opening or the sticky up end of the spindle will get in t'way.
2) Fit a simple, fixed, curved shield on the front similar the that on the Tauco linked to by Speedy Builder5. So long as the belt is adequately above hair height a front shield is pretty much as safe as a full cover. Especially if you run it round further to go past the side and partially over the top of the front pulleys in a similar manner to the Meddings Pacera L1 **LINK** (pictures about halfway down the page). Various Atlas models **LINK** were similarly arranged with a rather shorter shield.
3) The simple shield idea can easily be extended into a half or three quarters cover if you don't mind removing it to adjust the belts. Three slots, one at the front and one each side, with wing-nuts or wing bolts should be sufficient to hold it in place. Over centre catches and other fully engineered devices may be snazzier but I never feel the extra effort to get them installed properly is worth it for this sort of job.
4) At least one maker used a two part cover split lengthways with hinges on each side considerably reducing the overhead space needed for opening. I've seen one like this but unfortunately cant recall the brand.
Clive.