Code requires you have a receptacle every 12 feet along the wall (or to be more precise, located such that you can place an appliance with a 6' cord anywhere you desire without use of extension cords). You need to comply with that regardless.
I don't agree that an "access hatch" is sufficient; Code has certain rules for just how accessible junction boxes must be.
If you can make the old receptacle boxes accessible enough for Code, then you can extend off them via surface conduit such as Legrand Wiremold. You start with a "surface conduit starter box" then use surface conduit to go to surface mount junction boxes. They even make slimline receptable boxes only 1" thick.
Be careful to buy surface conduit at a real electrical supply house, the kind in the industrial district and no pretty mall ambience. You will need some of the oddball parts, and big-box stores just don't stock the slow sellers. The electrical supply will carry every part, or none at all.
Retire and permanently remove the receptacles, and install new ones in new locations.
Start by looking at products called "Old Work" junction boxes. Avoid the ones that only attach to drywall; drywall being essentially chalk wrapped with glued paper, they aren't strong enough to survive a wrestling match of trying to insert or remove a stiff 3-prong plug in a new socket. Look for the ones that attach to joists with stout screws. Big bonus points for metal boxes. Metal boxes don't burn.
Now with both Code spacing and "old work" box design in mind, select new locations for receptacles that are needed, or that you want.
No doubt the receptacles are wired in a string and there is already a route for Romex/NM cable through the various joists. Once you have the new boxes sited, push the cables out of the old boxes and demolish and remove the old boxes. Then do some workable combination of
- Use the old route of the existing cables to run an entirely new cable run between your new boxes, i.e. fishing a new cable. Or
- Join the old cables with a UL-listed-for-the-purpose splicing device, that is designed to splice inside walls without a junction box. There happens to be one, made by Tyco.
At this point the old junction boxes are gone (you needed to in order to get access to fish or splice) and there are gaping junction-box-sized holes in your drywall. Patch them in the normal way, or since the old junction boxes were mounted on studs, screw a chunk of wood into that stud, so that it can support a piece of drywall where you need it. Predrill holes to be sure the screws won't split the wood. Patch and mud; paint if you care.
The patching is mainly to protect the fire-stop rating of the wall. Being a fantastic firestop is drywall's one redeeming quality.