If Watford don't get a home Draw in R3, assuming they beat Reading in R2, then Vicarage Road would be an option.
It would only be marginally more acceptable to Spurs fans than MK. Playing at Twickenham would be attractive to Spurs fans because it isn't associated with any rival Premier League club. I'm sure quite a few Spurs fans will have put Twickenham on their survey responses, as well as groundhoppers.
If Spurs fans are really that against sharing another PL ground then there is always Brentford. This is a LC tie and isn't going to attracted 70,000 fans to fill Twickenham.
There is the option to ensure Tottenham get an away draw, thus making this issue go away. A numbered ball in the microwave for 30 seconds would ensure Tottenham are drawn away.