Try using your toaster’s bagel setting if it has one to minimize the toasting of the outside (I have no dog in the fight, just something I thought about)
That’s a great idea, and I would do it, but: after I bought my toaster I realized far too late to return it that the bagel setting is a lie. It heats both sides, it’s just adjusting the timer to be right for bagels. While still cooking both sides for not good reason.
It might be the angriest I’ve ever been at a small appliance, if you couldn’t tell by my sharing this anecdote almost entirely unprompted.