Joe-
Welcome to the OLF!
If you are making a 'replica' of the 37 Hauser, you'll want every detail the same, but if you are building a guitar based on the Hauser (Brune) plan, I wouldn't worry too much about the bridge differences between the LMI bridge and the Hauser.
IMO, You should think of the LMI bridge as a 'roughed out' bridge- there's plenty of finish work and shaping left to do. As you mention, shaping the bridge to the dome of the top will 'use up' a bit of the depth of the bridge.
On a first guitar, I wouldn't worry too much about small details like the difference in tie block length. Just make sure that the string separation at the bridge 'works' with the fingerboard width and taper in the plans. A quick diagram (full-scale) is a good idea for checking that, if you have any doubts.
BTW, it's the saddle location that's important (for intonation)- a mm or two difference in bridge location is not a big deal- so I wouldn't worry about the different amounts of wood 'in front of' the saddle.
The 'tilted back' saddle is considered by some makers to be 'better'- there's a tendency for the saddle to be pulled/tilted forward by the strings, and there are also ideas about having the string angles closer (in size) to each other on the two sides of the saddle.
Some possibilities:
Bridge blanks are quite cheap; you could buy a couple and make a bridge or two, if you want to take the time.
You could add a tie block overlay to the LMI bridge- keep it fairly thin, and you could take a bit off the top of the tieblock to make some room for an overlay. Solid bone (or ivory), or a bone 'frame' with a mosaic or other decorative inlay are both quite traditional looks.
Keep posting details/questions/pictures as you go- there are quite a few keen classical builders around the OLF and it's nice to see another build in progress.
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Cheers
John