There are options besides an "RV Shop" for much of the work you outline. Any electrician or shop that builds or repairs horse or utility trailers, or even UHaul
shops can do trailer lights
. Many plumbers also do gas lines, as do propane
suppliers. You may well save a lot of money by finding a pro with the tools willing to do a little side job.
On the trailer lights
consider purchasing the colors of wire indicated in the wiring diagram, and running the wires yourself, then pay to have them hooked up. The Bargman 7 pin trailer plug used by your trailer, is an industry standard and has standard wiring colors that are used for turn, running and brake lights
, Aux power for the trailer battery
, and trailer brakes
. Pulling the wire yourself you know what color is for what and where it runs, then the experienced person does the hookup and tests. Can save you money and leave you more knowledgeable about your trailer.
On the gas lines, you really need the interior, and probably the appliance(s) in order to properly run the lines. Typically there is one long line with T and L fittings along it to branch to the appliances. Copper tubing can only be curved so much in a given distance without kinking. So you would get the best results by knowing not only where the gas appliance is going but where on that appliance is the gas connection. I don't think "flexible" line such as is common for household gas appliances is typically used in campers, it is all copper tubing and flare fittings, probably because they are more vibration resistant. Worth a trip to YouTube to watch some videos on installing flare fittings on copper tube just to get an idea of what is involved and how it is done. It really is surprisingly simple process with copper tubing. Running steel gas lines in a house now that is a beast.
On my fridge
the T is on the right so the copper gas line coming off the T connection has room to curve back parallel to the main line and hit the fridge
connection on the left. Stove may have connection on side or front depending on the stove, could even be on the rear I suppose. Where the to put the T in the main line to route to the appliance is going to be pretty hard without the appliance and it's location being known.
Frankly if you can build a deck, and don't mind wasting some short pieces of copper tube to practice using the flaring tool you could probably do this. Pro or DIY they all check for leaks
using soapy water to see if a joint blows bubbles with pressure on it. Some plumbers have a fitting with a pressure gauge and air valve (like a car tire) and will put air pressure into the lines and check the gauge later to see the gauge shows any loss of pressure, but that is not typical outside of home construction (building inspector requires it) Campers and small jobs it's generally soapy water test.
I'm not disagreeing with those that say 110 volt systems and gas lines are something to leave alone if you are not comfortable with them, however it might not hurt to do some of the work yourself and just hire a pro to test or finish it. Anyone that is competent to wire lights and outlets in a house, garage, or workshop can do the same in a camper, consider making an arrangement with a friend, co-worker, or family member. With you as helper by the time it is done you will have gained a new skill, or at least some knowledge. After all at some point in your life you built your first deck right?
BTW - I am 100% simpatico with your "do it as you can" approach, takes longer but slow and steady progress can accomplish a lot over time. Took me 4 years to build a school bus camper, 5 years to build a finished basement, but the satisfaction lasts a lifetime and not having a huge credit card bill, why that's priceless