When I did my suspension upgrades I did the front first and the rear a couple thousand miles later. I don't see any big reason why you couldn't go the other way.
We have a newer wing and are going through the same planning myself.
I would definitely recommend replacing the spring on the new shock. When I put a new 2013 trike takeoff shock on my 2001, I went with the Progressive brand spring. I thought I read somewhere that the stock 2012^ spring (1000#?) has a higher rate then pre 2012 bikes (900#?), but still lower then the Progressive (1,100#?). At 290lbs, going up 200#s on spring rate should be good I thought. I could be wrong on the exact spring rates.
Once we did the 2013 shock/progressive spring combo we could run the pre-load in the single digits solo and teens 2-up. Was it perfect? No. The rear was a bit under dampened for the spring rate. The dampening on the new 2013 shock was notably better then the 80k 2001 shock. Was it better then stock? YES YES YES.
I have had properly matched spring and dampening rates on my other bikes (custom ohlins and wilbers). For a big touring bike, this is a great compromise. Bang for the buck it works.
If just putting a spring on the a OEM shock I would consider a HyperPro progressive spring, as opposed to the straight rate Progressive brand spring. I did the HyperPro spring kit on 3 of my bikes (CapoNord, CBR1100XX and Pegaso) and they rode great. Very smooth ride on on the smaller bumps and still enough spring rate to keep from bottoming. Unfortunately HyproPro only offers one spring and I suspect it was sized for average weight riders (as opposed to riders who are above average
This time? I have more money to spend and plan to keep my 2006 a long time. I am planning on a whole replacement shock (Racetech or Traxxion) with a matched spring.
I was an early adopter of the Progressive monotubes with spacers. Way better than the stock ride. Firmer, more controlled, no big shutter on sharp edged bumps. I had a local Honda dealer install them as well as new bushing and seals. As an aside. The mechanic and the store owner rode my monotubed bike. They thought it was terrible. Way to stiff. Sits to high, The mechanic rides a GL1500. The owner rides a GL1800 regularly. They think that the sagged out stock GL1800 is the best handling/riding bike there is. They are totally baffled why someone would change it. They sell a lot of "safety chrome" but never suspension upgrades
This time, I plan to do all balls, racetech kit and matched springs. The monotubes were very good, but I can spend a few hundred more this time.
Installed the shock/spring myself. I didn't confuse my friend at the dealer as to why I would ruin the stock GL1800 suspension. Took me about 8 hours. I work slow. I'd do it again.
For the front, a local independent shop that has done a lot of racetech and bearing installs will do the work.
Oh, I plan to do the front suspension first because I think it needs the more improvement.
All that to say, at your 2-up weight, I think it would be wise to put a new aftermarket spring on your new shock.