Nice to see! I read the ads regularly and might recognize this one . . it was for sale in?
I had (and sold) a 34' trailer thinking that not only was a shorter trailer more desirable, but one with a rear bedroom as well. I now would enjoy having a 34XB, or a 34X from 1989-90. Aero design (and IS) mean more than weight.
I'm in favor of going after all the hitch-rigging and tow stability questions first. Roadworthiness. The GVWR of this trailer is right up against the top of the DODGE ratings.
I haven't found any advice on the AL KO axles in re replacement (as per AIRSTREAM and HENSCHEN) either testing (by measurement) or otherwise (do a search here on A/S axle replacement). One correspondent wrote that he had contacted the manufacturer but had no reply to acceptable versus worn necessitating AL KO replacement. It's worth exploring further (not ignoring; the point of being on AIR is that there are enough folks here that someone
will have chased down information and not relied on some "doesn't need it" admonition/consensus in small groups).
I'd replace shock absorbers on the trailer if so equipped.
A disk brake conversion would be VERY high on my list. As would either a PULLRITE or PRO PRIDE hitch (looks like the trailer is riding nose high?).
I'd start with hitch rigging. An IS trailer needs to ride level! First item is solo -- empty
-- weight of truck (driver, full fuel and only what remains in truck at all times), then:
(There are many threads on hitch rigging -- and how to -- so be ready for more reading, but this is a great approach).
I also have a CTD (2004). Tire inflation on LR-E tires can be found in MICHELIN or GOODYEAR .pdfs to get tire pressure adjusted according to load (on mine it is no more than 50 FF and 70 RR for maximum loads; a 2WD) which is only from a certified scale. I use BILSTEIN shocks, and you might read up on a rear anti-roll bar for the truck. Also, if yours is 4WD then you may already know the tendency for the balljoints and steering to have appreciable wear by 100k. (cumminsforum.com or dieseltruckresource.com or turbodieselregister.com). Happily, these trucks have no need for tuners, chips, etc. An exhaust brake is on my short list for the truck.
Tire should be no more than five years old (many threads). I prefer CENTRAMATIC balancers on mine. Alignment should be checked by a big truck shop technician.
I replaced all the exterior signal & clearance lighting on mine with LED; a TRUE safety upgrade. (Some very good discussions around here on LED interior lighting as well).
The vehicle umbilical and safety chains are ripe for replacement if they appear questionable. (Search)
I am not too thrilled by the OEM hitch receiver (lateral forces may twist it under hitch tension), so, if I do not upgrade to a PULLRITE (have a Hensley), then I will change the receiver to a TORKLIFT or similar.
I see references to AVION roof sealing with ETERNABOND. Do a search around here as I compiled a fair amount of info on sealing chemicals on this site. Check especially at awning attachment points (dealer-installed item, often) and around entry door for soft floor. Also, dried (contracted) window seals.
"TXiceman" recently picked up an '89 34V, and is an experienced RV'er (although, as a FORD driver, you might take any advice with a grain of salt), and has his SILVER STREAK up for sale. He upgraded to twin roof A/C units and a 50A panel. He and his wife have re-done the floors, etc.
With two furnaces onboard I'd label that SYSTEM the first one tackled.
But the FIRST job is the WORST job and that is cleaning. Took me almost a solid week to wipe down every single surface.
RV'ers just don't do it, IMHO, and it's best to do at the very beginning; (they'd rather eat the depreciation and finance another disposable white box [a ten year trailer on a twenty year note]). I started on the ceilings (including behind cabinetry) with a dilute solution of CASTROL purple cleaner in a two bucket set-up. Then the plumbing (CLR on a rag), then the shower (GEL GLOSS), then the ovens, etc. Then the wood work (TIBETAN ALMOND STICK). Also made notes as to small problems (cabinet latches, drawer slides, etc) that otherwise never seem to get done. (Also a good time to inspect heat ducting hose). Etc (Found a new non-staining lubricant I like: JIG-A-LOO).
The battery system will benefit by a reading on this site. With, what,  batteries, the more careful one is here, the better. Read up on AGM-type LIFELINE brand batteries, panels, and converters, here and elsewhere:
BestConverter - Converters, Inverters, Electrical Supplies, Electronics
The more pics the better: roof, underside, suspension, water/electrical hookups, exterior storage compartments (lit and detailed; no one else on line has done this). Getting it aired out, cleaned out, and a detailed inspection of small things -- with photos -- is a great way to start.
Looking forward to it!