Is there any 3rd party solution that can sit between the two (I am willing to pay for the service), or can I achieve it myself?
If you integrate with a 3rd party, you'll still have to send the payment details. In which case PCI still applies.
PCI requires many different things and cost is high. So it takes time and money. what can be quick, short term solution and long term solution if needed?
If you are not actually storing the details, just transferring them, and you are processing less than 20,000 transactions per year then PCI isn't too onerous.