I sent BTC to a BCHSV address. is it lost?
No.
The process to 'recover' your BTC is to import the BCHSV private key associated with the address into a BTC client.
That's all you need to do to access them again.
However, since you do not own the private key (poloniex does), they are the only one being able to recover them.
It is completely up to them if (and for what fee) they recover your coins.
Exchanges often help their customer if the amount is high enough.
But it also would be completely understandable if they refuse to recover them, since this includes quite some risk on their site combined with additional work.
It all depends on their security model. Only a few people there have access to the private keys. Messing around with the private keys because of people not being able to read / choose the correct address and ignoring all warnings might or might not comply with their policy.
But regarding to their answer, they are trying to help you.
Technically, it is definitely possible.
is it safe to post the txid here?
It is, but noone else except for poloniex can help you regarding this.
The transaction id wouldn't help anyone.