Information about time-to-digital converters (TDCs)
This is the first I have heard of your "time to digital converter" thingies.  That is probably because I've never tried to look for a stand-alone part like this before, which is because just about all microcontrollers have this capability built in.

Many many micros have the capability to capture the value of a free-running timer on a edge of a digital input.  That seems to be what you want.  You need 50 ns resolution, so the timer needs to increment at 20 MHz rate at minimum.  There are plenty of micros that can do that.  Some of the dsPIC, for example, can run at 40 MHz instruction rate, which is also the rate the timer can be incremented at.  That would give you twice the resolution you need.

It is unclear if you want to measure the width of a pulse or the time between two separate events.  It also matters what the minimum possible time between the start and end capture is.  Depending on the answer, you can do this with a single capture module or you may need two for each pulse.  If the minimum time is long enough, then the firmware can grab the capture value from the first event and reconfigure the capture hardware for the second event.  If the time is too short, you need separate capture hardware for each edge, perferably running from the same timer.

Take a look at the "Input Capture" module of dsPICs.  One or two of these should do what you want.  You may not be able to handle all 6 signals in a single micro, but micros are cheap, so use one for each signal if you have to.  That also makes communicating the result back to some central location easier since you can implement any protocol you want.

For more specific recommendations we need to know what the minimum time between the edges are, how/if the 6 signals need to be synchronized, do they have a commmon start time, etc?