Most investors are not going to complain if you go back and give them stuff. Having said that, it's work.
Would definitely try to use the others as social proof that the term isn't required and exaggerate the amount of work to "renegotiate" with confirmed investors (btw, you're not renegotiating... the next time you send out an email, just drop a note that they're getting this bonus term - it's kind of a shrug anyway). If new investor still needs it and you still need investor then, depending on your circumstances, I'd point out that there are valid reasons why you'd want to defer an equity round such as you generating enough revenue to defer for higher valuation - should you be penalized for that? "It's important that my investors and I are completely aligned, etc." If that's a reasonable scenario then that should be enough. Even better when delivered with third party validation ("I was talking to an investor that has done a trillion deals and he said he didn't like the variable kicker because he's seen founders push for an earlier financing at worse terms just to avoid this extra dilution."). Less experienced investors tend to put more crap in and often need more experienced investors' wisdom to let it go.
The reality is that if you're 12-18 months down the road, you're running out of money and you're not able to raise money, then you'll need your existing investors to carry you. At that point it's a new deal anyway, so the extra 5% - 10% penalty for missing your funding timeline is completely immaterial. So if you can't move the investor off the term, then take the money, drop in a sentence in a future email to current investors and get back to work.