LR4 here, the screenshots might help with suggestions on how to obtain things in a timely manner. One thing to note though is that a lot of veterans like my self who have been playing for close to 10 years have been able to pace ourselves with the release of content to some degree. So while the total number of MR based items may seem high, it wasn't always the case.

MR30 here. Apart from the prime and lich stuff, there's definitely a few easy things you've missed, and some clusters of stuff you can work on simultaneously or while doing other things (like cracking relics or grinding aya):

• Have you done all the zaws, kitguns, k-drives, and amps? Wasn't sure if what you're using tracks them. If not, that's potentially a big chunk.
• BPs from the market: pandero, carrier, dethcube, shade, wyrm, various archgun/archmelees (parts require syndicates)
• BPs from the dojo: catabolyst, mios, helios, djinn, itzal, dorrclave, hema
• Nightwave: heat dagger, dark sword, wolf beacons for wolf sledge
• Deimos iso vaults: aurum spinosa, sporothrix, cortege, and necramech parts; rep for cortege and bonewidow BPs. Note that arcana iso vaults have better drop rates for aurum spinosa and sporothrix parts, but you'll probably be stuck doing them solo.
• Stuff from syndicates, all of which are tradable if you don't want to swap syndicates: various archmelee and archgun parts, sancti/secura/telos weapons, abyssal beacons for dorrclave mats
• BPs, parts, and relics from corpus railjack derelict caches: carmine penta and nautilus, plus relics for valkyr prime, nyx prime, cernos prime, scindo prime, hikou prime, and venka prime
• Baro: prisma weapons, vericres, halikar wraith, vulkar wraith, prova vandal, supra vandal, vastilok, ax-52 (probably)

As a side note for sibear, I found getting cryotic passively while grinding circuit much less tedious than trying to grind it directly, but that might just be me.

A really niche relic farm, some relics for the most recent primes can be found in Profit Taker bounties.
Check Profit Taker Phase 2, 3, and 4 bounty rewards, these missions are fairly short and have a reasonably good drop rates for their respective relics. You can open Nightwave/view lich to skip dialog gated parts of the quest.

Just some rough estimates for times:
Phase 2 ~2min
Phase 3 ~5min
Phase 4 3-5min

For phase 2, any speedrun warframe like Wisp/Nova/Wukong. Bring along a Shade or Huras Kubrow for their stealth ability. Best to play this mission solo, I find the game likes to load me into lobbies after the mission reward screen if I'm playing public.

Phase 3 only requires you to match the Profit Taker's element, more damage does not speed this up. Use whatever you're comfortable with.

For phase 4, use Chroma or any tanky warframe with Eclipse/Roar. Knockdown immunity (overguard/passive/ability) is nice but not a requirement. *If you find you aren't seeing a bounty reward screen, the Profit Taker is taking too much damage from a single shot in one of the archgun phases, try switching to the Imperator/Mausolon.

These missions are mostly just an alternative to playing a mission like Disruption/ESO. The tradeoff is that you don't really get burner relics but any relics that you do get will be radiant. The other nice part about playing these missions is that you don't need to deal with waiting for the right rotation for your desired relic to become available.

If you need a weakened version of one of the infested companions, you can use the Tranq Rifle (sleep arrows only temporarily put them to sleep, Tranq Rifle is infinite duration) to put them to sleep and then attract an infested to the area to attack them. I would use Ivara to go invisible once the infested are alerted, If you're brining a companion for something like enemy radar, it should be a sentinel without a weapon so that it can't accidently kill the infested before it converts the Predasite/Vulpaphyla to their weakened version. Look up the cycle needed to spawn your desired variant or try your luck with Pheromones.

The last thing is if you can do is work on multiple things at the same time like rank up weapons/companions while collecting relics like in ESO to make things a little less grindy. Passively get relics through spending syndicate standing, or while cracking relics in the void. There's a chance someone runs a relic you need and this can end up saving you a lot of time. And take breaks whenever you need them, there's no reason to burn yourself out just to reach some mastery rank.

There are certain weapons I consider platinum only, specifically because they are locked behind a piece of content that has too long of a lock for me to keep my eyes open.

Specifically, I'm referring to things like the Arum Spinosa, Sporothrix, and Deimos Archguns, as you need to run Arcana Vaults, which might as well be solo only, and annoying/boring as well. The Ambassador and some Prime warframe (Ash?) parts are behind 20 min Railjack Survival. Vandal Lato/Braton are at the end of 20 min ESO. In addition to being mind numbing, it's also very easy to fail/get lesser rewards from these missions.

I would generally only subject yourself to a grind if the secondary/tertiary rewards are worth something to you. Running relics is almost always worth your time, regardless of mission type. If you need to level some MR fodder, run some Void Cascade or Duviri Circuit so you're also getting Zariman Arcanes or Circuit rewards, as well as big bunches of Focus.