I’m so sorry it sounds like you’re “between a rock & a hard place”! You desperately need to keep your mobility but need a reliable car to do it. What’s the point in spending money on a car that is likely to pack up!
It cost me £500 to have the conversion done but luckily my car is a Mazda (i.e. reliable!) and an automatic, so it wasn’t really a difficult decision to make. I think from what you say it may be worth appealing the PIP decision - how would it be if you had to wait another, say, 4 months for a decision? In the worst case, if you are still turned down, do you have a garage nearby who would do the conversion? After they’ve ordered the parts, it only takes a couple of hours to do the work so it could be done within a couple of days (although it takes many weeks to get use to - I’m still finding it a bit scary after 2 months!).
It makes me so angry that “they” say “they” want to keep disabled people independent, but when it comes to it, “they” don’t - grrrrr!