Alright, any idea what I am looking for once I open the case?
Have not looked inside a BC780XLT, so I can't say for sure. If it's a metal cased crystal; it would be marked on the board as "X-1", "X-2" or such. It would NOT be the one that is marked as "10.7" on the body of the crystal as this would be the 10.7 mHz IF crystal... assuming that Uniden still uses 10.7 mHz crystals as the IF oscillator.
In later models, it is more likely however, that it would be a blue or tan colored ceramic resonator somewhere between 4-8 mHz (could be higher too) and would likely be marked on the board as "Y-1", "Y-2", etc. See attached pic of ceramic resonators. Would really be best if you had a copy of the service manual.
May not be the source of your problem at all but, these devices (and their associated circuit) are certainly possible suspects when citing scan speed problems.