The best approach is to eliminate the open overflow and provide a sanitary rupture disk on the top of tank with a discharge line to the floor/drain. This will prevent overfilling, or overpressure due to any problem. A high level switch will still help avoid high level problems and prevent the disk from breaking in all but the most unlikely cases. The tank will always be sealed, breathing only thru the vent filter.
HOWEVER, I don't know the type of tank you have and what, if any, pressure rating it has. If it is a very low rating, getting a sanitary rupture disk rated to burst before the tank does may be expensive or problematic.
Another option, if you have a tall tank, is to put a rupture disk on the bottom end of your overflow line. Regardless of the rating of your tank, if the waterlevel goes high and runs into the overflow line, it will generate a head on the disk equivalent to the height of the line. If the line is 12 feet vertical heigth, the column of water will produce 5 psig on it. A 5 psig burst pressure is reasonable. Note that you would not have, or want, a U bend in the overflow line in this case. Note that this approach is only for ambient DI water in an indoor location - so that condensation would not occur in the overflow line and accumulate above the disk.
Your last idea of a small continuous flow of water into the liquid seal would work and would be an inexpensive method to maintain a seal in the existing system.
The issue of tank going negative and sucking water in from the seal could be prevented by oversizing the line, and in most cases would be very unlikely. What would be likely using this type of vent seal ia that, due a problem with the vent filter or a much higher draw rate out the the system than you have predicted, you get a level of vacuum that exceeds the height of water in your U bend. You would then get outside air bubbling thru the seal and into your tank. The air would represent a source of contamination. More importantly, you probably would not even be aware that this was happening.