Well maybe you should reconsider the entire house. You say it was built in 1930's so we are talking a plumbing system that probably coming on at least 80 years old. Just about the right age to start showing its real condition. You don't say but I assume it is probably cast iron, probably never been upgraded.
Basically what you probably got is a questionable plumbing system no matter what anybody sezs or the amount of testing. If you have ever gutted an old house and really got a good look at what is in there for plumbing of that age it is pretty revealing. They never are what you expect, never have the proper vent lines, especially for the smaller lines, cast iron can actually sort of rot, never enough clean outs, never properly trapped, just not something that you would build or accept today. In effect a lot of them will be a sort of jury rig by today's standards.
So the fact this vent/trap is an issue might just be the tip of the iceberg. I am always very leary of older houses of this age that have their original plumbing, wiring or heating systems. That also includes the water systems. That is based on too much experience. Once you get the house apart you will find all sorts of weird stuff.
I just rehab'd a house I bought, built in 1923, not that far from your house age. If you first looked at it, as you would for some type of house inspection, the plumbing didn't look all that bad. Not enough clean outs but it appeared the main cast iron lines had been replaced sometime during its life. Looked like be ok, save some money, this could be serviceable.
But once I got things disassembled it was an entirely different story. The main line run in the second story did not have the proper slope, had standing water, the cast iron was relatively new but was showing signs of rot, some pin hole leaks, lead drain lines from bath tub, sink, a real mess. The plumbing run they had used didn't have prayer of working, needed to be entirely redesigned. Nothing that looked like a proper vent system. The typical type situation you find in way too many older houses once you get them apart. I've done a bunch of total rehab's and none had a serviceable plumbing system once you understood exactly what was there. Always got a complete new plumbing, electrical, heating, one rule of thumb is if it is older than 50 years, time to do a complete upgrade.
You probably got what is so common today. Older house where they focused on making it pretty. You see a ton of them, never upgraded the utilities, just covered over what they considered unimportant. Your situation is typical of a type of thinking. About like you state, make the kitchen more pretty, sort of push the trap thing to the back burner. Spend that money where it counts.
The problem being the houses are never reliable. Always something jumps up to bite you. And it never is easy to fix, more like catch as catch can, always more jury rigging as a solution. If the older houses are properly rehab'd before being made pretty, they can be super reliable, very energy efficient. Mine works better than most new houses, nothing breaks, never any problems. So moving the trap / vent might not be that big an issue, lot depends on the habits of the peeps there and what they flush down the lines. Some places those type traps / vents are illegal but even that is weird because they more or less base their thinking on more modern systems. I can see it either way, if the trap is installed as the concept is as designed, it works, the catch is always all the other foobaas old systems will throw at you.
Plus that cost seems way out of line. For a bit more, should have been able to have redone the entire system properly. I did my own completely for probably a few hundred, just paid the material costs. The most horrible thing that can happen to you is make the old house pretty, then have to try to finally fix either the bones or utilities. Nobody ever tells you truth when buying an older house and the importance of the stuff that you can not really see. Beware if they are telling you old utilities systems are no problem. If I wanted to sell you the house, I would be saying the same.
I've seen a bunch of houses with those type vent / traps, they work, the problem typically was the same, somebody paved over it, covered it with something and you could not get to it if needed. Murphy's Law always comes into effect. When you need it the most, it will not function and not be able to be fixed. Lot of them were a bear to get the clean out plugs out. You need a lot of room to get some leverage after heating them bit. Nothing like old plumbing to make your day.