My last trip discovered that the tugs are happy to "dredge" their way along.
They do not stop if you are stuck ahead of them but barge right on through, missing your brightwork by literal inches....

Many times I would see them comming and slide carefully over until I felt the slimy, shoaling edge of the center
depth... let them pass, move into the now swirling center of the ditch and wait a few minutes in the turbulence, then tuck in a hundred or so feet behind them. It's a bit tough on the
steering system for a while but slowing down until the turbulence was tolerable and then matching their speed produced good results most often... Some would even acknowlege my presence by
VHF and chat about what was ahead.... Best one took me from the
Georgia state line to St Lucie Inlet and into Stuart FL.... He laid up at
anchor for the nights too. But I did not ground the
boat at all with him ahead of me.