Presumably you have received an EIS3 (or EIS5) form for the investments? (I doubt you can claim relief without one).
The government's current information on claiming EIS here (via here) states (my bold):
If you made an investment in shares issued during the year for which
you have not yet received a form EIS3 or EIS5, you cannot claim relief
for that ...
Slight side-step to your first question to highlight your second:
"Alternatively, if I just leave the extra $1,500 can I claim it next year when my contribution room increases?"
Yes, you can do this, and I would say it is the recommended approach.
Technically, if you have no fear of miscalculating your RRSP amount, you can happily use the $2k '...