Lateral to Improve PE Recruiting/Improve Resume

After graduating in May 2020 and working in Big 4 Advisory, I lateraled to Raymond James/Blair/Harris Williams level TMT groups this past August/September. I am thinking about recruiting for PE next year but am not sure my current groups will give me the best shot at top PE firms - I am not 100% set on PE recruiting and could find GE or VC quite interesting alternatives. I am thinking about trying to lateral to Qatalyst/MS TMT/Evercore TMT/GS TMT type of groups next summer to improve my chances at PE recruiting, get a better name on my resume, and work on bigger more complex deals. I am hesitant because I worked at my previous employer for less than a year due to start date delays from Covid and will have worked for my current employer for less than a year if I were to leave next summer. I would then be working at the Evercore/MS TMT etc. level group for two years. I am fully aware that it is not an easy task to lateral to those kinds of groups and am not assuming that it is guaranteed if I were to pursue it - I would also be content at other top BB/EB tech groups but would certainly prefer the ones listed. Please let me know any thoughts or concerns about whether pursuing this lateral move would be a good idea.