That Lemond with 853 steel should be a great base to work with.
I think you're already realizing some of the issues with the conversion. Changing brakes and shifters. But, I think the overall result should be nice.
Older bikes have a benefit of having stem shifters or downtube shifters which you don't have to mess with. Also, some brands such as Motobecane often had fender clearance on most of their bikes (especially if you convert from 27" to 700c).
Nonetheless, your Lemond is a good bike.
As @
dabac & @
Wilfred Laurier mentioned, 9-speed Shimano is pretty compatible across systems. You already have a triple crankset.
As far as clearances for different tires, you have the bike in front of you. Most of us can only give you generalizations of what to look for.
1/4" or so of clearance on all sides of the tires would be nice, but you can go down a bit more, especially if not riding on lot of gravel or fresh tar.
There are other bar configurations that you might look at. For example, people have used a variety of brakes and shifters on "Moustache" and "butterfly bars".
With a classic quill stem, vintage friction stem shifters are also possible, and dirt cheap.