OK, the pictures help A LOT.
Those tuners are hard to work with because the part of the tuner which comes in contact with the wood of the back of the headstock puts plastic on wood. Furthermore, the plastic which contacts the wood there is convex rather than flat which makes it almost impossible to put in a washer. I have those tuners on a vintage Regal and they are hard to deal with.
So, you need to look at what you want to do with this instrument.....
As for keeping it original....for me, as a vintage uke guy, I HATE when someone puts new tuners on an old uke. I want it as original as possible, and then if I am going to make changes, I can do it the way I want it. So, if you think you will be selling this at some point, either leave it alone and try to make what you have work a little better, or only make changes that don't alter the uke so you can put it back to original to sell it.
If it is a player for you, and you intend to keep it then consider changing them to something that will make it work for you day in and day out. You can go with some good Grover tuners and you would likely have to widen the holes. However, I have had great luck with Ping brand friction tuners. The shaft is thinner than Grovers and they may drop right in. The Ping tuners I put on a vintage uke of mine are smooth as silk when tuning.
One thing with the Ping tuners. They come with a washer for the top of the headstock which needs a countersink hole. I abandoned those and bought a pack of stainless steel flat washers at the hardware store, and used those on the top of my headstock. They match perfectly and eliminate the need to countersink the hole, and thus, dropped right into my uke. Ping tuners can be had for about $10.