Circular to linear

Subject to permission from the satellite operator you may be allowed to operate circular polarisation. You must ask first and they may well say no.  If you do, you will lose half your transmit power, so you will need twice the HPA power compared with linear operation.

On receive, you will degrade the performance substantially as the amount of signal received from the satellite will be halved.

To convert the antenna to linear polarisation may be difficult.  Two options are (1) to remove the polariser and replace it with a plain tube or (2) turn the OMT by 45 deg so that the linear polarisations of the tx/rx wave guides lines up with the polariser slots/pins.
Unfortunately, neither of these options may be practical or feasible if you have some complex feed system with separate 4 and 6 GHz polarisers.  Very high quality 4/6 GHz feed systems may not be easily 'adaptable'.

Contact the antenna and feed manufacturer for advice.

A brain-storm idea (rather imaginative  ) You might consider using two external 10 MHz  reference PLL LNBs and somehow merging the L band outputs, probably resulting is a narrow useable bandwidth.

Yet another idea (simple) added later ! ...

Take out everything behind the circular tube feed horn waveguide flange and replace with a rotatable VSAT OMT. (2 port)

More ideas welcome ....