If the hospital has a pager system it is usually very strong.
In audio options in Sentinel, other software or directly from your scanner you might consider doing CTCSS / DCS Search for your conventional freqs. Often this is the default for Uniden radios so you may have what I am going to describe already.
When you have done the above as the scanner scans it will display any found CTCSS tone frequency in your display. If you enter those found tone frequency in the audio options for each appropriate frequency your scanner will not stop on interfering signals but only on stations that use that tone to activate your squelch.
I had hospital pager problem a few years back and that is what I had to do and it worked great.
If some of your problem is bleed-over then you may need to buy some mono-frequency filters and put them on your coaxial cable (between you and the antenna) to reduce the signal strength mostly of just the frequency the filters are cut to. I have had to do this on a DOT transmitter only a block away.
I have also used a 14 element 2 - meter beam and turned it to null out an offending transmitter and it worked pretty good to in eliminating an interfering signal.