Hello. I am also a RDM main that has to deal with the fact that RDM is mostly pushed to the wayside, especially in the last year. I'll give you a few suggestions, although most of the best gear is not (easily) soloable.

-Egeking fully augmented gives a huge amount of accuracy if you find yourself needing some. It's better than most other options when accuracy is an issue.

-Nibiru Blade (Escha Ru'aun T2) is a great sword to have. Try to get a party for it.

-Fettering blade is a great main hand sword that gives great stat boosts (and it looks cool).

-Ginsen from the Tenzen 2 fight is a must have. Lupine cape from Fenrir 2 is great as well. You can spam them both during the campaign on Normal or Easy. Partying for Difficult or higher will yield better results but I got both from Normal.

-Now is the time to spam Alluvion skirmish to get augments on your Claideamh Solius and Taeon sets. Unless you can get hold of Carmine+1, Taeon is pretty much the best melee RDM can get.

-You can buy Voodoo Cuisses and Greaves for Carmine+1 (roughly 10m each, which is waaay cheaper than most HQ abjurations). You'll need to obtain the abjurations from T1 and T2 Escha Ru'aun NMs (shout or get a party) but they are well worth it. The NQ versions (probably under 50k each) are useable if you don't have 20m (or want to spend that much on 2 pieces of gear).

-Ambuscade cape- get at least 3 (1 for enfeebling, 1 for nuking, 1 for melee, and possibly a 4th for weaponskills)
-Accessories that are easy to obtain: Brutal Earring (Ancient Beastcoin exchange), Suppanomimi (Divine Might 1), Asperity necklace (Delve), Rajas Ring (CoP story).

-All the better accessories will require a party: Petrov Ring (Escha Ru'aun T1), Dignitary's Earring (Reisenjima T2), Combatant's torque (Combining all the Warder torques in Escha Ru'aun), Sanctity Necklace (Reisenjima Domain Invasion), Reiki Yotai (Escha Ru-aun Kirin), Hetairoi Ring (Reisenjima T3), Kentarch Belt+1 (Unity), Sarissaphoroi Belt (Reisenjima T2)

-Might be worthwhile to make an Excalibur (easiest REM to solo)

That's all I can offer for melee at the moment. If you want advice on magic sets I can do those as well.