First off welcome to the forum.
Before you start working on your grandfather's Krag I would recommend hanging around here for a while and going back through some of the older threads.
Second, I do not think heat would help removing any Krag barrel. They butt up against the internal stop in the action, and I do not think you will find any that will take any kind of cheater or real torque to remove. Heat can damage things so I would not do it.
I have seen some sporterized Krags that looked nice with bluing, but original Krag actions were not blue and a restoration with blue does not look right.
  Others that are more into collecting will comment on the wisdom of trying to restore something that needs so much work. If it is a bucket list thing for you maybe, but I have my doubts as to whether it would be monetarily a good thing.
Personally I think it might be a better goal to get it back to a hunting condition. Hunting with a Krag will make you smile.
If the scope mounts line up, a good low power scope might be the ticket.

'Sniper338' - Welcome to the KCA Forum. You have been given good advice by 'madsenshooter' and 'FredC'.

If you post some nice clear/close-up pictures of your 'family heirloom' Krag, you will get further suggestions, guidance, and assessments.

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Were the clamps holding the stock together actually holding the hand guard on? I did not see a break in the stock. I was going to suggest that in other threads repairing stocks has be quite extensively discussed.
Also barrels originally thought to be worn out can shoot very well with a little experimenting with bullet/powder combinations. Maybe with cleaning you have already discovered it is better than your first impression.

'Sniper338' - As others have stated, this Krag is a poor (and expensive) candidate for restoration. A 'drilled' receiver pretty much ruins any original restoration attempt.

I am left wondering your motivation for replacing the barrel. How long is it now and what is the bore condition?

To honor your grandfather, it would make sense to put it into a good configuration for Hunting. This could be done rather inexpensively, if it has a decent bore.

Your receiver holes look like they were done for a Weaver side-mount. The Weaver #2 side-mount base (#48402) is still made and sometimes shows up real cheap on ebay. The Detachable Side-Mount, (#49350), also is still available and is a solid way to put a Scope on a Krag.

Your stock 'chip' could be repaired near the receiver ring. A walnut nose-cap or tip could be added to the stock at the barrel-band to give the stock a carbine appearance.

A krag rear-sight and 'banded' front-sight could be put on the barrel to have iron sights.

The description of your hand-guard problem puzzles me a bit.

Attached is a picture of the Weaver side-mount and an inside view of a Krag hand-guard. I hope these are of help. BTW - Your hand-guard is for the model 1901 sight.

(p.s. - It appears a lot of your Krag's parts are retaining original finish. Krag rifles and carbines did not have a homogeneous 'Blue-Black' finish like many more modern arms have. IMHO - Putting a modern finish on a Krag does not turn out well).