My first question here and you pros are a kind, patient bunch. I have spent hours reading explanations to similar problems and I think my issue is my pipes being too small but I was hoping for a little advice.

I have a 1929 house and a Maytag washer in the basement. When it empties (via a tall standpipe through a p-trap then into the drain line) I can see water slowly work up the nearby floor drain (about one foot away) and eventually come up just a bit making a small puddle that very quickly goes back down as soon as the washer has emptied. There is a utility sink connected to the same drain/vent. After reading about similar problems I pulled the washer discharge hose out of the standpipe and let the washer empty into the sink thinking it would slow down the flow (I was amazed at how forceful the washer emptied). That indeed stopped the overflow but water still comes right up to the top of the floor drain.
I turned on both H and C on the sink at full blast and I couldn't duplicate the floor backup. I filled the sink and emptied and no floor drain backup. Nothing else in the house backs up, and nothing else appears to use this drain line. The washer/sink drains are properly vented. The standpipe never overflows. The whole system is 1-1/2" but the old metal pipe coming out of the floor the drains connect to looks wider (like 2-3").
I disassembled the sink/washer drains and snaked the drain and floor drain 25' and both were clean with no resistance at all. I took a hose and ran both H and C on full blast down the floor drain and standpipe and no backup. I can't find any way to duplicate this slight overflow. And I'm reading here about how powerful new machines are and I have old 1-1/2" plumbing.
Is there any way to slow down the discharge rate of the Maytag? Maybe reduce the discharge hose diameter to a smaller size and/or add a few turns? Increase the standpipe length? My floor drain is just a hole with no grate or cover and I can look right down it. Is there a device I can place inside or on top of the floor drain that will prevent minor backflow yet allow the drain to function properly? Like a flap or a ball or one-way valve or something I can retrofit?
Thank you for your time and any advice you could provide would be greatly appreciated.

It sounds like you have covered all bases here and that you have actually found the answer to your own question. The washer does output the water faster than it can drain away. If you cover the large hole in the floor with some sort of check valve the water will just back up to the stand pipe and make a bigger mess.

Either the drain pipe is too small in your older home or there is a restriction more than 25 feet away that your snake could not catch. Restricting the washer discharge hose is an option but mainly as an experiment, the washer will continue to drain the water until is senses that the water is all discharged, be it slow or fast. Is it feasible to make the hole in the floor bigger to hold more water, it sounds like you are on the verge of it just barely overflowing at its current size, but I think in the near future with more drainage build up that a bigger hole will also be filled to its limit and the entire drainage system will require constant maintenance.

Of course you want to wash your clothes on a regular cycle and not a delicate cycle that may have a gentle spin to discharge the water slower.

A strange idea would be to drain the washer into a hog trough and the hog trough would have a hole in it to drain into the hole in the floor, the smaller of a hole you made in the hog trough the slower the water would drain of course BUT over time it may start to smell?? My mom drains her washer into a double set of sinks next to the washer where one sink probably holds the same amount of water as the washer with no clothes in it, no mess. GOOD LUCK

Ask your neighbors who they use, to find a good plumber! You want one that can clean out your main drain. If you are sure that it is vented as it should be then it is a drain obstruction and may be more than 25 ft. down line. If you get a good plumber , he will take care of your trouble. Kentucky Nick

I don't think you have a clog in your pipes. We have had many complaints about the more powerful washer pumps overpowering a older drainage system. Yes they do make a flood preventer for floor drains,(see image). Check them out at;Flood guards for floor drains - check valve to prevent flooding from FAMOUS PLUMBING SUPPLY
If you still have a problem with the standpipe backing up and overflowing I have a repair for that too. Just click on back. Good luck, Tom

I like Tom's solution, it starts to seal up what was an open system. I'm going to guess your stand pipe will be the next leak as Tom has hinted. Might as well do both fixes at once and get it over with. OK Tom show him your next pics.

Duane - thank you! My floor drain is recessed and sloped like a shower so the water stays in about a 12" circle at it's worst. I also realized this is only a problem when I run a load on the highest water setting.
Eventually I'm going to have to bite the bullet like most of my neighbors have and get the whole system updated.

Tom, thank you so much for responding! Every post I read had an expert answer from you. Also read your posts about using a clamp on the standpipe to make the system a closed one when it's the standpipe that backs up. So, would it be OK (not cause any harm to machine or back up water into utility sink, etc) to say install the floodguard on the floor AND use the clamp on the standpipe if needed?
Either way, the floodguard looks exactly like what I was hoping was out there and I'm ordering one.

While I was typing this I see ballenger answered my question. I'm going to use both the floodguard and the clamp. This is an amazing forum and you guys are awesome!