The acceleration service is have used is viabtc for free it works perfectly for me but that is only when your transaction fee is less than 40 sat/byte it was share in our local board by @Charles-Tim.
Less? It works fine as long as it's above 10sat/b (not vbytes), you can accelerate even a tx that is 100sat/b if you are bored and have nothing to do for 10 minutes.
The issue is, there's currently no user here in Bitcointalk that reported their experience with mempool.space's accelerator.
It would be great to have some legitimate feedbacks.
AFAIK, their accelerator isn't
fully open to the public yet
[the feature in question is there, but as soon as you create and verify your account, they'll put you on a waitlist (almost one week and counting...) and that means you can't even top up your account (unfortunately)].
I hope they add LN payments for that, the whole thing is a bit messy for those accelerators, if you can't send or receive money because you paid a low fee and now you need to pay a higher fee to get a payment though to get that previous one confirmed it turns to
funny situations like this one:
Imagine you have some hosted wallet on an exchange, the dumb mofos send your withdrawal to your wallet with 10sat/b and now you need to accelerate it, you only have BTC there so you make another payment to mempool.space but again, the idiots send the tx with 10sat/b. So you need to accelerate the tx that should have paid for the acceleration