Okay, last comment for a while, I promise! (I really do, I need to run to the hardware store before it closes). I finally got you a log! I saved it to SYS:, so this time, when it crashed, at least I had something recoverable for you! Enjoy! 
(note: it crashed during the process of scanning for fonts, before the application had even fully loaded. If I run it without -V, from Workbench, and from the ram disk, it usually runs better than this. That seems to be the "winning combination" for me, right now
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OK, it looks like it crashed after the font scanning, but because -V with the file redirection tends to buffer in memory, the end of the file is cut off (not your fault - unfortunately redirecting from stderr isn't possible on OS3, so getting NetSurf to write direct to disk is the only option). You can try -v (lowercase), which will output to stderr so we can see where it is crashing.
I think your font "unable to open" problem is that you have a designed bold/italic font defined in an otag file, but the font itself doesn't exist (because the log is from a session which didn't get that far, this is a bit of a guess). I might be able to add a fallback for that condition, and I don't have a clue how to add (or remove) these on OS3 (on OS4, TypeManager has the options to do it, I don't recall the same in Intellifont but it might have them).
Not trying to sound like a smartass here, but if a program fails when using the latest versions of libraries and utilities, chances are I don't want to run it. Life is too short to be flipping around libraries and whatnot, just for one program.
But, I'll keep playing around with it. Sometimes I like a challenge. 
Well, I did say it was alpha, with a big warning about saving everything

How do you change its cache and memory options? Oh, it uses fast ram on mine, all right. About 53 megabytes worth (most of that as cache), just to load Google! 
In users/Default/Choices (might be users/something-else/Choices) you can set:
disc_cache_size:0
That will disable the disk (disc) cache. If you've been running the installer, you'll find it creates the Choices file for you with a couple of entries, so it should be easy to find before you run it.
What filesystem are you using? I'd like to know why it is crashing when on HDD.
It might be worth trying it on HDD again with the disk cache disabled, in case it is that causing it.