I did replace a centerboard once, but I was able to do it with the boat on the trailer. I do bottom paint our current boat (over 3600lbs) , and I do that on the trailer, and don't worry about where the bunkboards cover the bottom. It seems that the anti-fouling paint does scratch off if pressure is applied. It seems that painting the bottom and then rolling it around on the painted surface to turn it upright could scratch up that newly painted bottom.
We once sailed in a 17' Siren. For several years, I used that boat trailer to carry firewood logs home and then cut the wood into pieces at home. To get the boat off the trailer, I made several wooden pieces to hold the boat in the air and allow me to move the trailer out from under it.
I lowered the front pivot wheel to it's lowest position, then measured the distance under the stern of the boat to the ground. I then made a well built, padded wooden platform that would just slide under the stern of the boat. Then I jacked the front pivot wheel to it's highest position, now the stern was supported on the rear platform.
I then picked a spot about 2/3 of the distance from the stern to bow, and measured a distance from the boat to the ground where I could install a jack pad. I made two solid jack pads, one for each side, such that they would not slide outward or tip over. I would slide these into position, and then attach a flat brace on the ground between them, for additional support so then would not move outward. The jack stands had to be placed wider than the trailer. Then I would lower the front pivot wheel until the boat was fully supported on the rear and side jack stands. Then I would carefully pull the trailer out from under the boat.
I wanted to use the trailer, but it did leave a boat fully suspended boat in the air where it could be easily sanded and painted. I would only do this with a small boat if I was going to work under it.
This could be modified to be simpler and still work if you have a solid hoisting point for the front of the boat. Follow the first several steps, but do it under the hoisting point. Then with the brace under the stern, and while the boat is jacked up in the front, tie a strong rope, come-along, or chain from the hoisting point to the front eyebolt. Now when you lower the front wheel, the boat would be supported by the stern brace, and the front rope/chain. This should allow you to move the trailer around enough so you can eventually sand and paint all of the bottom, without special side supports, or completely removing the trailer. I would probably add a small, movable safety platform under the front of the boat.
Just thought of another method, again using the stern support. Have the boat supported off of the trailer on that stern support. Then (presuming you have one), use a hydraulic car jack with a special v-shaped, padded wood brace under the front of the boat and lift it up. You should be able to move the trailer back and forth enough to reach all the area you need to sand and paint. Then when you remove the front and rear bracing and the boat is back on the trailer, you can paint those spots blocked by those supports.
If you are not handy, or don't understand safe and strong supports, it would be better not to try these methods. You don't want the boat to move or roll over while you are under it.
I just happen to enjoy these kinds of challenging projects. My skin is not thin, if anyone finds flaws in my thinking, they do me a favor by pointing it out.
I also owned a Javelin and still have the glossy brochure. length=14'; beam=5'8"; draft=6" to 3'10"; sail area 125sq ft; base weight=475lbs.