Multi-Band
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I do not have a direct answer to your question. Downeast Microwave use to make a interface device to allow both 2M and 70cm transverter on a single XVTR port. I am not sure if they ever made a 2M/220 version. Additionally, I am no longer sure if Downeast Microwave is doing any business at all. It seems they have passed some products over to Q5 signal and that company has a few interesting products.
If you really deeply into VHF/UHF with your Flex and you have extra $'s looking for a place to go you might consider spending alot more money for a lot more capability and buy one of their multiband transverters.
A phone call to either company might yield a solution but I suspect your fall back of a manual switch would be the least expensive and quickest solution.
Of course you could also purchase a used 6300 and run the 220 transverter on it or upgrade your 6400 to a 6600 which has two XVTR ports. I suspect you already know this but thought I would mention it anyways.
Good Luck, John K3MA