The way around this problem is for the Tea Party to present the four challengers with an agreement, that by a date certain, whichever of them leads in a “pre-primary”, as judged by a poll of the Tea Party membership, or even registered Republicans, will become the single nominee, and the others agree to drop out and give their support to him.
They either sign the agreement, or they are immediately cut off, and are no longer endorsed by the Tea Party, and those who do sign can call them “spoilers”, and reject them as nothing other than agents trying to get Graham re-elected as a “dirty trick”.
Yes, it is serious, but it is also good strategy. If a candidate cannot control their ego enough to support another candidate who is better than they are, they do not deserve to be elected.
No need to narrow the field down just yet, the primary is designed to do that.