Does your VCR have a built-in RF modulator? if it does and also have A/V outputs? If so you can feed the A/V outputs to a second RF modulator (or a VCR since those have RF mods built in), set the internal modulator to ch3 and the external to ch4 feed each modulator to its own 3-way splitter then feed each output of the splitters to a different set. I think if you tried to split only one consumer grade RF modulator 6 ways you would be short on signal strength. If you want to go uber cheap and only run one set at a time just use the one RF modulator and get some TV antenna switches.
The expensive and time consuming to set up (there are threads here on VK about it), but more extensible method of RF supply is to buy one or more Blonder Tongue AM60 (agile/channel selectable) or BAVM (fixed channel) family RF modulators, set up a transmit antenna on the modulator, and a receive antenna on each TV set.
If you plan to have vintage TVs in other rooms setting up a BT agile modulator to transmit over your entire property is a wise choice. I have over 70 TVs split over 3 rooms (+garage in summer) on 2-3 floors and a wired signal source scheme is wildly impractical for me. I have enough agile modulators to send 6 different channels ,with at the moment, 4 configured to operate. Basement channel is fed by a VCR, cable box, video disc players and some videogame consoles. Upstairs there is a whole rack of sources (U-matic, SuperBeta, SuperVHS, CED, LD, DVD/HDDVD, Bluray, cable boxes, DTV box, PC with S-video output in its graphics card, etc) feeding 3 other agile modulators in transmit mode. I literally can put almost any video format on almost any (and certainly an unlimited number of) screen(s) in a block radius of my house.
I recently got a free used server that can support 4 PCIEx16 graphics cards (I have 7 such cards with S-video output) and am considering making my main TX rack computer controlled, and primarily computer supplied.
As for power...Do any of your sets need that variac and how many sets do you want to power simultaneously? I am not above turning on enough sets to trip my breaker and have done so repeatedly
(2-4 different programs on 2-4 different vacuum tube color TV sets drawing 200-600W each + a rack of AV gear and a 1KW PC power supply or 2 will trip a breaker)...But you probably want to plan your loads to avoid nuisance trips. If more than 1 set needs that variac you will need to assess how much current draw those sets have and make sure your variac can handle* what you intend to run on it at once, and the same goes for your breaker(s). Current draw is rated power consumption divided by wall voltage (though the numbers printed on TV sets are not always accurate so measuring is advisable). Your breaker and variac (also the power strip) will both have amperage rating. If your outlets are on different breakers powering all sets at once should be much more practical than through a single breaker. Also consider the needs of any lighting and or other rooms/outlets on the breaker...If your TVs are the only things on that breaker you may be able to power them all, but if that one breaker is powering a hair dryer, and or PC, and or vacuum cleaner in that or other rooms you may be able to trip the breaker with only one TV.
*If you have steady line voltage and are simply using the variac to drop or increase the input voltage to one or more of your sets then your wasting a variac. Instead get a heater transformer with an output voltage that is the difference between what your wall voltage IS and what you Want it to be...Then wire that flament transformer as either a buck (reduces output voltage) or boost (boosts line voltage) autotransformer. If your line voltage fluctuates then a variac is still not the optimal way to do it...They made and make line isolation transformers that regulate their AC output voltage (they go by a bunch of different names VRT, CVT, etc, and most are made by Sola) and they will take anything from 80-140VAC input and spit out rock solid constant 120VAC (or 117V on older models), and will hold that output constant through any input fluctuation in that range even if a cycle or two of AC input drops out...Best of all it is fully automatic so you never have to dig out a DMM and tweak a variac to keep your sets at some intended input voltage (also your TV picture will never again bloom when the fridge or AC compressor kicks on...Or in my case when the industrial park half a mile away turns some huge motor on and off randomly 45 times a minute for a few hours on end). Used VRTs can be found cheap, but new ones are stupid expensive so go used if you can.
The above should reduce your issue to 1.) better defining your needs/resources and 2.) doing math and shopping.