Cura will just deal with inside walls differently.
In Meshmixer whack the Solid Accuracy right up and make the mesh fairly dense 250 or over, and choose accurate instead of fast. My ageing MBP only takes a minute or two to figure this out.
There are a couple of dips on the surface after this which can be smoothed out by selecting these point and using smooth (under select>deform in meshmixer).
Whenever you ask a program like meshmixer to figure this out on it's own it's going to look at all the geometry and thats why it creates dips in the surface where it has seen an inside wall.
You can get a pretty good print out of it however.
This is kinda patching a problem you have made for yourself however. A better way to sort it out might be to create a flat svg of your font in illustrator and then extrude this in blender. But I'm not sure how you would do the curved edges on the font (I dont use blender)
Or try to pick up a solid modelling software and do it with that, as making a solid out of a basic geometry would be easy in most solid modelling software.
Here is an stl created in Fusion 360 for example, process being
Sketch Text (select 3d, separate the letters)
Extrude (will create a solid for each letter)
move letters together
combine (into one solid)
rule fillet face (history must be on)
create underline
combine
You could achieve something similar in the free 123D Design as well.