When I switch pre amp tubes, I don't pull the chassis out. I disconnect power and speaker cables, put a blanket on my coffee table, put the head on it, roll it end over end twice so it's upside down, remove power tubes, remove pre tubes, then reverse the entire process.
You can't fit your fist in there, so you have to learn how to hold the pre tubes between your fingers, I use my index and middle. This is for getting them in and out of the chassis, and into position in the tube socket, but not for inserting and removing.
I use a flashlight to help see, then I put my hand in flat, palm down, and curl the tips of my fingers and thumb around the tube as my hand enters the head cab. I use a gentle circular/spiral/rocking motion to ease the tube up out of the socket, but not all the way. When it's just barely still in, I then go to the index/middle finger scissor hold, and take it the rest of the way out of the socket and then the head.
To insert, I grab the tube with index/middle, aim pin one of the tube to pin one of the socket and guide my hand flat, and palm down, into the head then chassis, lower the tube into position and when it's lined up, use a little finesse to get it seated enough that you can let go and change your grip. I seat the tube fully by flanking the nipple of the tube with my index/middle fingers or thumb/index, and use the same gentle circular/spiral motions.
Go slow, steady, and smooth, like the game operation. Once you get it down, it's not hard. Sometimes I'll change tubes two or three times a day when I'm experiemting, so I like to be able to get it done without removing the chassis.
I hope this helps.