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I do mostly sports/action so not sure is helpful my experience.
I use 1Dx III quite a bit on a Ronin S and if I want shallow DOF I use 50 1.2 and 24 1.4 so the mode that I pick is 5.5k 24 or 25 and on a gimbal I never notice the RS.
I did track so far Parkour, MTB, Horse, rollerblades and never notice RS issue. If I don't need shallow DOF and/or need wider I use the 16-35 and f5.6 or above so I then switch to 5.5k 60 fps to have slow motion.
In case I need both I use 4k 60fps crop.
As you have the 1DC the weight size is about the same so you know what it means on a gimbal plus you are used to MF so using 1Dx III 5.5k 50-60 is not an issue for you.
The big question is how are the 4k FF 25,60 and 120 modes of the R5... if they are very good I think the R5 is even better than the 1Dx III....... if the FF 4k modes are binned and not super quality then the 1Dx III is better especially if you need 50-60 fps....
R5 advantage over 1Dx III (mostly guesses😞
- less weight
- flippy screen (not too helpful on a gimbal but is good to have)
- zebra
- 8k vs 5.5k
- quite cheaper
disadvantages:
- less battery life
- 60fps max out at 4k, if binned it will be less quality too
- if it has a 1-1 crop it will be 2x
- larger file size in RAW
- no RAW > 30 fps
- probably no dual card video recording (on 1Dx III the only dual recording mode is when in RAW.... as it does RAW in one card and whatever 4k mode you select on the other (from 8bit h264 to 10 bit h265 LOG).

If you are not in a hurry I would wait the first reviews hopefully will be in July .... and if you are undecided maybe rent both.... 

So far I find the image not a HUGE step up from 1D C, while very good in 4K and 5.5K RAW especially, the 1D C MJPEG 4K 8bit stands up well today. The 1080p is pretty naff and not any better than the original 1D X and 1D X II 120fps.
No 4K crop though, and H.265 offers much more manageable file sizes. The 10bit is better for Canon LOG.
I found myself with a lot of the recent mirrorless cameras 'hankering' for my 1D C. Not very rational! But I love the chunky DSLR build quality, OVF and the 1D C's thick chunky image, big files, amazing colour, so cinematic.
Maybe the 1D X Mark III will be thought of in the same way once I've finished comparing it to the Sony A9, A7 III, Leica SL2 and Fuji X-T4. I'll have to keep giving it the benefit of the doubt for now.
It replaces quite a lot of my stills cameras so may justify itself that way too.
Don't forget to add £500 per 512GB CFexpress card to the price though.