No, unfortunately not. But didn't they tell you your (preliminary) bahn.bonus number after you've signed up? I don't really know the process, but when you order a BahnCard, you'll get a PDF printout with a preliminary BC number that should be good for collecting points (unless you have already purchased your ticket).

The only way, as you have already figured out, is to cancel your existing ticket at the cost of EUR 15 and get a new ticket at the current rate. Your reservation will still be valid, but of course useless.

However, you could purchase an upgrade ("Übergang 1. Klasse") during your train ride from the conductor. While I don't know whether you'll only pay the difference between a full-fare 2nd class ticket and a full-fare 1st class ticket or the entire difference between your ticket price and the full-fare 1st ticket (plus an on-board fee of ~10 EUR) and maybe even an EUR 15 refund/exchange fee (which I'd say is more likely), I wouldn't recommend this as this will most definitely become more expensive than cancelling your existing ticket.