PE recruiting for delayed start positions after accepting immediate start offer

Currently a 2+ year analyst in IB and did not recruit for PE until this year for various reasons. I accepted a PE associate role at a smaller platform for a 2020 start in a couple of months through offcycle recruiting, mainly because I didn't want to stay in IB any longer and the uncertainty of PE jobs around COVID. I am confident that with my background I can land something at a larger platform with better comp. I am still getting headhunter emails about 2021 opportunities, and I am contemplating signing up for those as well as potentially participating in on-cycle recruiting this year.

Long shot here, but does anyone have experience in participating in delayed start buyside recruiting (positions starting 1 or 2 years later) while in IB and with an immediate start offer in hand, with the expectation of potentially staying at the first buyside job for a year or two and moving on afterwards? And for anyone who does, how did you communicate it with your headhunters (were you honest about your situation or did not divulge your plans), and did it pan out / was it worth it? Apologies in advance for the convoluted situation, but looking to see if anybody was in the same / similar boat...