How many lumens does an incandescent halogen bulb provide?
Your calculations are correct, and you should probably figure on about 5000 lumens. Projector bulbs aren't expected to last nearly as long as, say, overhead lights, so they are driven harder for greater efficiency.

However, be warned that getting your optics right may be more of a challenge than you realize. A good condenser works on a small light source, such as the glowing filament, but LED bulbs are a much larger source since they use a phosphor coating on the bulb envelope. This will make it much harder to get good light concentration on the slide, and you may have to use a more powerful LED than you had originally thought.

It's fun idea though. I wish you luck.