Can a "separation offer" be negotiated for "termination" not layoff?

Hi there

NOT LOOKING FOR LEGAL ADVICE

I'm in a weird spot. I'm a software engineer and have been in the industry for 20 years. I'm in my early 40s and was "terminated" for " performance, not meeting the expectations of a senior engineer". Per the terms they'll give me about 7 weeks of pay if I agree to waive all claims esp the ones related to ADEA.

The lawyer I consulted advised to first just reach out and ask for a better offer without escalation. Is it reasonable to ask for pay thru the end of Dec? I won't say it's X money for Y months but that I think me signing away my rights is worth 3 months of pay given

1. I was not given any warnings about my perf
2. A cursory look up of my git commits, chat and meeting history will prove I was actually quite active working on projects I was asked to work on, and completing them.
3. The company is doing poorly - upper management has been shuffled and they also need to invest in a ton of new hardware for maintenance and growth
4. Good luck finding a job in this market in Q4 where I won't be "overqualified"

I'm not going to mention any of this of course but that's my internal calculation. I understand they don't owe me shit and can ask me to pound sand but it doesn't hurt to ask - so how much more to counter with?