Good question!
if you have a Flexible budget, it could still be within reach!
As you know the problems we are all facing In this hobby is the availability of quality parts! The 16610 is no longer the hot thing in town as it has been replaced by that goofy new tuna can style ceramic insert model 116610 - the in thing amongst peoples with more cash than $#*#$. Finding a close to 1:1 spec is going to be very difficult unless you can trace down a pre owned item that no longer buzzes on the owner!
if I really wanted to spend the money, I would buy a star supply case and as many parts that come with the case at star supply as this case is designed as an aftermarket replacement for the 16610 which should fit the genuine 3135 movement!
if you have plenty of change left' you may probably still find a pre owned 3135 with some luck, but if this is not a necessity to your build I would buy a genuine eta 2824 which should fit this case, but the real problem is getting the right case ring which was once made by TC ( who seems to be either retired from the watch hobby or for good) to accomodate the eta movement in a genuine spec case! This ring is a must, but again finding one is going to be challenging unless someone else has also cloned this ring! I have been looking for one since TC went West or East!
The other avenue you have is to be on the hound side to buy a pre owned one in the sale Section of this forum! Sorry that this isn’t much help but it is what I would do if I really really wanted a great piece that runs circles over the cheap quartz copies
good luck!!