Want to change the headstock or neck on my '79 LP?

I suppose you could do this.  You could find a LP with the neck you want and see if they could swap the necks for you.  It would be hard but not impossible.  I think my biggest fear is you love the tone of this guitar now and its special, what if you reduce the size and the over sized head stock was part of the magic that made it have that vibe it had?  Honestly something as old as that guitar I wouldn't bother.  Its 33 years old and is like a diamond in the rough.  My opinion is I wouldn't touch it.  Aint broke don't fix it.  Just like the Fender Strats with the boat paddle head stock some people think they are ugly some don't my first question is how does it sound?  If it sounds great play it, if it sounds bad move on.  I don't base my guitars on how they look or how I'm going to look with them strapped on my shoulder because nobody is going to care if its got a creamy tone coming from it.

But he said he lives in Ireland and it would cost more to have it shipped and come back in and such.

Ted179, my suggestion would be to keep the 79 stock, and try to trade it for something that fits your likes.  For example a an early 70's,  1950's reissue (look it up, they exist).  Or sell it outright and get a custom shop aged something or other in time.  I am not against mods, but in the end, if you have to cut into the wood, or add wood, you are making so many changes to the existing guit, that it will just not be the same instrument; it plainly will not sound the same, so all the "mojo" and all of the currently great things about it, in the end, will be gone.  The reason the guitar sounds good now is because of the the wood, shape, and electronics.  Changing electronics is a reversible thing, but seems like removing and adding wood, the headstock being purely cosmetic, and the neck shape changed... yikes.  If for some reason you did not like it, in terms of feel (something that cannot be predicted as i recently touched a custom shop 59, and then a real 59 burst and they got the neck shoulders all wrong, and if Gibson themselves can't do it right...) there is no way to go back, and your guitar will be worth jack didley squat in the market.  Just my two cents since you asked, but in the end we have to fall many times to learn to walk.  Now if this was a new off the shelf guit, i would say "play ball".  Don't cut the old wood!!!