I know that you are right about bullet velocity being somewhat less important than accuracy and fun. My favorite rifle is a 62 cal flintlock--definitely slower than any other rifle I know, but I shoot it every chance I get because it is fun. So i know you are right. 

But I also want to avoid making a big mistake that could hurt myself or others. Some people have told me to go ahead and rebarrel to a 45-70 or 38-55. Without the input from this forum, I would have proceeded down that path. I'm very thankful for the input above that keeps me on a safer path. 

Your honest question has helped me to better understand my issue with this gun. Upon inheriting it, I expected to use it for deer hunting just like my grandfather used it. But last Tuesday I found that the barrel was ruined. I reluctantly decided to replace it but today found that the barrel is unsafe for the action even if it were in good condition. So now I'm faced with spending $300-$400 to fix a rifle that I can't use for deer hunting or varmint hunting. It's taking a while to adjust my expectations to this reality. I'm still unsure if it's worth $300+ to have a rifle that shoots 38's. But this seems like the best option if I choose to use the rifle. The real problem isn't the rifle but my expectations. I didn't expect to have to pay $300+ for a fairly beat up rifle that shoots 38's. You've posed an honest question that I need to Consider before making any more steps. THAT is also one of the benefits of a forum like this. 
Please don't take offense at my rantings. I think your insights are right on.

Joe, if it was a piece manufactured in 1889, wouldn't it be a small-thread, flat side? I don't recall if any were different. 
Some high walls had small threads, but the other way on low wall, until the later Winder version?

In my youth. well I wasn't that young but it was a long time ago, I had a low wall in 22 K-Hornet. It was a lot of fun and I never pierced a primer. Someone offered a barrel in 22 Hornet. If the barrel shank size (the part that screws into the action) is correct and the price is less than a reline or new barrel, that might be a way to go.

I'm unsure if this photo will help answer the question, but it looks pretty thin at face value. But remember that this is a 45-70 chamber.

There's a highly recommended smith about 1-1/2 hours from me who can re-barrel or reline the existing barrel. I've made an appointment to take the rifle to him next Wednesday. I'll avoid making any decisions until I get his input.

One more question before taking it to the smith:

If I ask the smith to re-bore the receiver for a large threaded barrel, would I have a few additional calibers that I could choose from?

I just finished reading a series of postings on the marlin owners forum relating to the pressures produced by a black powder 38-55 cartridge. The are saying that the pressures are about 17,000 psi max. This sounds entirely within the limit for my LW. Even a 38 special produces more than that. I would just need to get the barrel stamped "for black powder only." I use BP in my flintlock so I do not mind loading it or getting the barrel stamped for it. 

Is this a possibility for me?