You now have an H23? You say you had a San Juan, so I am describing this for the Hunter 23.
It is not that hard to step and raise the mast, and there are various posts and videos you can find that show how to do it. Do you have the mast crutch that goes into the rudder pintles? If so, the general idea is:
1. put the crutch in the pintles and raise it as high as it can go (if it is adjustable height)
2. loosen all the stay turnbuckles as far as you can - just make sure it isn't so far as to not support the mast (which would be almost impossible, I think, unless you removed one completely)
3. rig a line with a pair of double-blocks, like maybe the main sheet, from the bottom of the jib halyard to one of the fittings on the bow, like the pin at the front end of the anchor well, on the deck. Extend the halyard so it is long enough to reach near the front chainplate, and cleat it at base of mast. You may have to buy a pair of blocks and some line. I run the loose end of this "lifting" line through one of the jib sheet blocks to the jib winch and cleat.
4. Pull the line with the double blocks as short as you can make it (blocks as close as possible to each other), and fix end to the jib cleat in cockpit. Tighten the jib halyard with the winch to slacken the front stay (or roller reefing rig, if you have it). I have roller reefing, and found it easier to remove the sail before doing this, though the prev owner did not.
5. remove the front stay toggle pin, at chainplate
6. use the "lifting" line to gradually lower the mast - the double block arrangement gives you the mechanical advantage to hold it. You will need maybe two or three people to help steady the mast side-to-side as it lowers, since the side stays no longer provide any support (and get looser as you lower it).
7. once it is lowered into the crutch, remove the mast pin at base of mast. Note that it may not be possible to get it all the way into the crutch without the mast hitting the roof of the cabin, if crutch is too short. Make sure the helpers can hold it while someone removes the pin - it is heavy.
8. carry base of mast forward so it is in "crutch" support on bow pulpit, and so stern crutch supports top of mast. Remove and secure stays.
Various people have rigged gin poles or other supports to help increase the angle of the lines, as did the PO of my boat. He made an aluminum bracket that wraps around base of mast, and extends about 6 inches in front of the mast (basically, a U shaped piece of aluminum sheet that is maybe 1/8 inch thick - must have been hard to bend). He drilled two holes through bracket and mast (which I don't like) and bolted bracket to mast. He used a pretty robust aluminum pipe (say, 2-3 inch diam) bolted with two bolts to bracket, so it sticks straight forward (that is, horizontal) when mast is raised. The pipe is sized in length to be about 3 or 4 inches short of the forward stay. The front end of pipe has an eye bolt vertically through it with eyes on either side. The halyard attaches to top eye, and the lifting rig line to lower eye. This way, the angle of the lifting line is much higher and easier to manage. I have seen a video on You tube showing the whole process, and this author used two pipes (metal electrical conduit) forming a inverted V, with the two lower ends of the V atatched to the forward lifeline stanchion bases, and the upper tip of the V supporting the halyard end and lifting line respectively.
On the other hand, if you can safely tow it to the yard and not have to remove it, why bother? While tuning the rig when you launch and re-raise the mas isn't all that hard (well, I have only done it once, as a new owner, and am not sure it is actually "perfect") it does take some time. If you don't race, and I don't, "good enough" tuning seems to be the objective, and mine seems to sail OK - not too much weather helm, etc.
The tuning process I used (and don't take this as gospel from an expert):
1. lift a long tape measure all the way up halyard - I bought a cheap 100ft reel tape at Harbor Freight tools for like $7. Attach loop at end of tape to halyard shackle, and attach safety line to shackle in case tape measure breaks.
2. If you can (I did not, as I was forced to put boat in water before I could) use front stay to adjust mast position front to back so mast has about 2% rake rearwards. Use a line frm top of mast and weight (like plumb bob) to see where line "points to" on boom, and it should be about 2% of distance from boom to where line attaches to mast. E.g., if that length is 30 ft, distance from mast to point of weight would be 2% times 30 ft).
2. adjust upper side stay turnbuckles so mast is vertical side-to-side, by measuring length to each side chainplate until about equal. Tighten these turnbuckles so they "feel tight", and mast upper bends slightly aft. As you tighten, the swept spreaders push the mast forward, so top bends back. As you tighten, make sure you turn both turnbuckles equal turns, and recheck mast centering when done, using tape measure.
3. tighten inner side stays so mast is straight by looking up the mast main sail groove. I fould it fairly easy to see when it is pretty straight, and as you tighten each side the inner stays pull the center part of the mast side to side.
4. tighten rear stay turnbuckles
Search for other threads on tuning - there are a lot here, from folks with much more experience than I. One season of raising and tuning does not an expert make.