Solartron 7071/7081 FS is 1.4
I didn't realise the full range was 1.4 - I assumed it was just under 2
100k range: 3ppm reading + 1ppm of range
(3ppm + 140k/10k * 1ppm) + (3ppm + 140k/100k * 1ppm) = 21.4ppm (first reading + second reading)
1Meg range: 4ppm of reading + 1ppm of range
(4ppm + 1.4/0.1 * 1ppm) + (4ppm + 1.4/1 * 1ppm) = 23.4ppm
10Meg range: 10ppm of reading + 1ppm of range
(10ppm + 14/1 * 1ppm) + (10ppm + 14/10 * 1ppm) = 17.7ppm
This sums up to 80.2ppm for the transfer + 10ppm for VHP101
Therefore even with the 24h specifications the reading should be 10Meg +/- 200ppm and not +300ppm
You keep assuming that the 7071 is perfectly linear on ohms mode, even though there is no specification that says that it is.
Without a linearity spec, you have to add the error for a 10K resistor on the 100k range to the error for a 100K resistor. You cannot just say "I am only looking at a relative reading so I will chuck out the absolute accuracy term". The thing is the 100K reading may be out in one direction, and the 10K out in the opposite direction and the meter is still within specs.
So on the 100K range, here are the errors:
10K resistor - 20ppm + 1ppm of fs = 20ppm + 1*(140K/10K) = 34ppm
100K resistor: 20ppm + 1ppm fs = 20ppm + 1*(140K/100K) 21.4ppm
Add the two together and you have 55.4 ppm. That is a very different number to your 21.4ppm error. 55.4 ppm is according to the specification sheets the worst case amount the 100K resistor reading could be out when compared to the 10K reading on the 100K range. It is not 21.4ppm
I haven't included a 24 hour specification. It is not really needed if you do the transfer in one go and you repeat the two readings several times to ensure there is no extra drift in the short term. That is one specification you can get rid of.
If the 7071 was linear to within 1 count - as you seem to want to assume - why wouldn't the manufacture want to proudly publish this fabulous performance in their specifications? I gather they do specify linearity for volts, but don't for ohms. There is a message in that.
It is possible to get greater accuracy then the specifications if you test the meter and find out what its true linearity is. But to do that you need something that has a known absolute relative error - such as $30 of resistors matched to 0.1% in a resistor transfer box. I haven't suggested using the 5450A since it would add a whole lot of extra errors into this process. The 5450A would be over an order of magnitude worse then $30 of resistors wired as a resistive transfer.
The point I am trying to make is 1ppm accurate resistive transfer is not actually that hard or expensive to achieve with the right methodology. With relays, you probably could automate the resistive transfer method. Below 10K, the contact resistance becomes a big issue, and at high resistances, the relay leakage current is an issue. You always have to take error sources into account.
If you can live with the relatively big errors your method will introduce, then your method is completely fine. The possible errors will just be much higher then you have been hoping.