I echo Steve's advice for hiking around Horseshoe Meadows to trigger the acclimatization process.
Which route up to San J did you take?
Cucamonga is a good analog for an ascent to TC short of the altitude being some 4K lower.
When I've been in my average hiking shape I've taken 2.5-3 hours to reach TC on day hikes with little acclimation. I'd have estimated an overnight load would have taken me about 4 hours. The latest I'd be comfortable starting would be 8 AM.
The longest time I ever took going up Whitney as a 5 hour slog to TC. I turned back at Keeler Needle that trip. That one took me 16 hours in total. If I had had an overnight load that day would have taken me 6.5-8 hours to get to TC.
YMMV though.
