Under your scenario, Trump would cut a deal to make Kasich VP and add his 220 delegates to Trump's 1050 and that would kick the tally up to 1270.
Game over.
This was suggested today by Randy Evans of the RNC on NPR. If Trump doesn't hit 1237 before the convention, this is what the RNC is planning for.
It doesn't work quite like that. The vast majority of Kasich's delegates are REQUIRED by their states to vote for him on the first roll call regardless of if he drops out / endorses Trump / dies / comes out as a communist / etc.... After the first roll call, many are legally allowed to vote for whoever they want. It depends on how they were chosen as to who they will eventually support.
The 66 from Ohio were hand picked by Kasich himself. They are loyalists and will probably do whatever he tells them to do. The other ~160 are picked by state parties, local voters, caucuses, etc.... They may not be as inclined to follow lock-step with what Kasich asks them to do.