When I tweak the nut on my ukes that need it, there can be a substantial improvement... definitely
you can improve the C string as that is the one that is off the most only by working on the saddle and the tech probably wouldn't do that for you anyways as it may need to be compensated... Maybe a tech would do that. I have never done that but it means sloping or making a knife edge under the string to get rid of that 15 degree error in the harmonic. The rest of the strings are not wrongly intonated, they are just having to be pushed down to far. Actually, its possible if that C string has an error at the nut as it might be not sloped properly either, then that might even help instead of the saddle.... (possible) but you gotta fix that nut first.
Its also possible that even putting on a set of Martins will improve the intonation because they are thinner. Its not like these shops are fitted out with Wizards normally in my opinion. So, if the fact the strings go a bit too sharp is bugging you, then that can be fixed quite a bit by setting it up by filing the nut slots. I wouldn't pay a guy 70 bucks to do that. I would get a two dollar metal nail file from Walgreens and just do it myself. You just pull the string out of the slot and move it to the side, file it a little like I said, check the height and try to set it, lower it like I said and do that for all the strings. If you do that, thats all they can really do for you in my opinion. 70 bucks is ridiculous to do that. You can do it yourself in ten minutes. Just work it real slow though and if you can be happy with the uke for now, maybe even postpone it until you might feel comfortable doing it. If you fret the strings on the third fret, do you see a lot of space between the string and the first fret? Enough so you see the string deflect say if you try to press it down to the first fret when its fretted on the third? You want it to just barely touch. Thats where you will get the most bang for your buck. After you fix / lower the nutslots, then if you want the strings even a tad lower, so you have less sharpening when fretting, then you can file the bottomside of the saddle with a piece of sandpaper and improve it a bit more. You can do all this over time as you get comfortable.
But thats what it needs in my opinion.
After you do it all and want to see if you succeeded, when you test it to see if its improved, just push it low enough to get the string barely fretted don't push down to hard. sometimes you can get a false indication if you do that.