First, the SL-T8000 is an 11 speed system, not 10. The right, rear shifter will have 10 clicks, but that's correct for an 11 speed system (starting at the smallest cog, it will take you ten clicks to reach the largest of 11 cogs). You're correct that the 22.2mm clamp will not work on the wider drop bar. I don't know of any after market clamps that will replace the current clamp and fit the drop bar. For the Shimano XT, T8000, to replace the band on the shifter requires a new top cap assembly (the upper, outer portion of the shifter). The shape is very specific with matching screw holes, etc and the shift indicator, if present, is yet another separate piece that would need the correct connection holes to fit back onto a replacement clamp assembly.

Finally, the ergonomics of a flat bar shifter mounted on a drop bar are not ideal. They may work for some if mounted on the top, straight section of the bar (and we've seen how they won't fit a drop bar without extreme modification of the clamp band). Another bug-a-boo is that the T8000, utilizes the cassette spacing and derailleur shift actuation of Shimano mountain bike 11 speed, both of which are different from Shimano road 11 speed. This can be over come by using a MTB 11 speed rear derailleur and an 11 speed mountain bike cassette.

By now, it should be obvious that simply trying to use mountain, flat bar shifters has some hassles that make the solution more of a problem. You might be better served by acquiring "bar-end shifters." These are designed to fit into or on the ends of a drop bar. They're offered in 9,10, or 11 speeds.

Another option would be to get a 7 speed mountain cassette or freewheel, depending on your rear wheel hub design, that has a 34 tooth large cog.

Changing your current cassette to one of these would be the most economical solution as it only requires the purchase of the wide range cassette. The rear derailleur might be out of its spec limit for number of teeth of the largest cog, but typically can be made to work just fine by screwing in the B adjustment screw to get enough space between the derailleur jockey wheel and the largest cassette cog.

You're correct that the 22.2mm clamp will not work on the wider drop bar. I don't know of any after market clamps that will replace the current clamp and fit the drop bar. For the Shimano XT, T8000, to replace the band on the shifter requires a new top cap assembly (the upper, outer portion of the shifter). The shape is very specific with matching screw holes, etc and the shift indicator, if present, is yet another separate piece that would need the correct connection holes to fit back onto a replacement clamp assembly.

Finally, the ergonomics of a flat bar shifter mounted on a drop bar are not ideal. They may work for some if mounted on the top, straight section of the bar (and we've seen how they won't fit a drop bar without extreme modification of the clamp band). Another bug-a-boo is that the T8000, utilizes the cassette spacing and derailleur shift actuation of Shimano mountain bike 11 speed, both of which are different from Shimano road 11 speed. This can be over come by using a MTB 11 speed rear derailleur and an 11 speed mountain bike cassette.

By now, it should be obvious that simply trying to use mountain, flat bar shifters has some hassles that make the solution more of a problem. You might be better served by acquiring "bar-end shifters." These are designed to fit into or on the ends of a drop bar. They're offered in 9,10, or 11 speeds.

Another option would be to get a 7 speed mountain cassette or freewheel, depending on your rear wheel hub design, that has a 34 tooth large cog.

Changing your current cassette to one of these would be the most economical solution as it only requires the purchase of the wide range cassette. The rear derailleur might be out of its spec limit for number of teeth of the largest cog, but typically can be made to work just fine by screwing in the B adjustment screw to get enough space between the derailleur jockey wheel and the largest cassette cog.