Staffers/Hiring Managers - Is this Grounds for Offer Rescission

TLDR: Would leaving off 2 IB experiences from my resume justify an offer rescission?

Need guidance on how to think about my career trajectory.

I began my career in a group I hated. Looking back, I lateraled out of my first group too quickly (~4 months) and ended up in a group that wasn't doing too well. The brand name in my second group was better than my first group and I actually enjoyed the culture, which is why I made the jump. 

After ~6 months, I and other members in my second group were RIF'd.  

Took 2 months to find a third IB role, but, admittedly, the brand name of my third and current group is not strong, the deal flow sucks, and I do not like working on pitches 24/7. While my current role pays the bills, it certainly won't develop me professionally.

I'm considering lateraling to a stronger bank in ~6 months so I can strengthen my resume and recruit for buyside. 

As I think about making this move, I have to be objective about my background and the implications of it. In particular, I think that having lateraled once and then being RIF'd and then having to recruit from a weak bank is not a very compelling pitch. To optimize my chances of lateraling to a better group and eventually recruiting for buyside, I am thinking of leaving the first two experiences off my resume and only putting my current role when I begin the lateral process. Doing this would (1) eliminate fear of flight risk from the interviewers' perspective given my short tenure at both shops, and (2) rid my candidacy of the RIF stigma. Furthermore, I would also omit my graduation year to get rid of the gap.

The consensus on WSO is that your resume is your personal marketing document and not a background verification form.

I think this is an overall solid plan, but I just want to know if I am allowed to do this before I devote a large sum of effort into lateraling again.

Any advice is greatly appreciated.