To make work 11m dish C-band dish, in Ku band

Contact the manufacturer. Ask about feasibility. The surface accuracy of the main reflector will need to be good enough for Ku band operation.  If feasible, get a quote for a replacement feed and subreflector, inclusive of retrofit assembly, alignment and testing. Make it the responsibility of the manufacturer to get your antenna to pass its acceptance tests with the satellite operator, before payment.  You do not want an antenna that fails its sidelobe patterns or cross-pol tests and cannot the used.

Consider the alternative of using a 6m Ku band antenna. Buy new, buy secondhand or rent an already existing antenna somewhere.

Also consider putting your data transmit/receive equipment at someone else's teleport, anywhere in the world, and controlling your equipment remotely.  Many hosting teleports (e.g. https://www.satsig.net/sms-teleport/sms-teleport.htm ) will already have a large antenna pointed at your intended satellite and all you need to do is rent rack space next to other companies doing the same thing, all sharing use of a big dish.

If your requirement could be met renting a fifth of an iDirect 5IF hub consider becoming an iDirect VNO.  There are opportunities. Many teleports have spare 5IF slots with hardware ready set up.
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Best regards, Eric.