Some thoughts about adjustable mandolin bridge setup (also applies to archtop guitar bridges):

Above is your basic adjustable bridge. A vacuum fit is essential to good sound transmission. We assume its feet have that vacuum fit to the top under tension If the feet fit the top at rest, understand that the top will change shape under tension and that nice tight fit will no longer be perfect when it's strung up to pitch.

Here the top (AKA saddle*) is lowered all the way—the thumbwheels are adjusted all the way down. Note the remaining clearance under the center of the top of the bridge. 
     (*There are too many instrument parts called a saddle, which is why I prefer to call this part the "top")

What can you do to lower it further? would be best if you didn't have to do this, but if you are careful, you can cut away a bit of ebony from just above the thumbwheels so the center of the bridge drops lower and touches the base, like this:

I've left a white line in this sketch to indicate there's a seam, but in fact the wood is touching wood. The thumbwheels are now little more than a decorative element, and the bridge is basically one piece. The point of cutting underneath is to preserve the intonation profile on the very top where the strings make contact.

If doing that means it's still not low enough, you can now begin lowering the top, which will entail recutting the compensation setbacks for the courses, and recutting grooves for the strings. This is often desirable anyway, but one thing at a time.

Lowering a bridge like this is semi-quick and dirty, but it works, and has less of a deleterious effect on the volume than you might think. A lot of Montana-era Flatiron A-5s seem to have this issue - a less-than-ideal neck angle resulting in a bridge that can't be adjusted quite low enough.

Ideally, one would reset the neck so the bridge could remain tall and adjustable and its top remain structurally strong.

Let's look at this issue again.

Cracks happen. Wood is wood. There are limits to what one can do to avoid problems. That said, even nice tall bridge tops sometimes crack if the grain of the ebony isn't parallel to the flats of the thumbwheels. That sharp corner in the inside of the cutout where the cracks typically start creates a stress point and is a slight design flaw in the first place. Making the bridge from bad wood or at least wood with diagonal grain is a flaw in execution. 

If the action is pretty close when the bridge is adjusted down fully, you can lower the action another final bit by cutting the bridge top under the wheels. However, if it becomes too thin, the string pressure will make the bridge swaybacked, overpowering the wood, and it will crack:

At the very least, a reduced bridge top will not sound very good. And if you later have to raise it up in order to correct the action, the string tension increases, and the bridge top is even more compromised.

Steve Smith at Cumberland Acoustics makes a "Lo-Boy" bridge that has a lower base so that the top remains more robust.

Here's a somewhat risky tweak on bridges, especially applicable to archtop guitar bridges.

If you can keep enough wood above the thumbwheels, it's possible to take a little bit off the underside of the ebony above the wheels to exert slight pressure on the outside of the wheels themselves, like this:

This sketch is an exaggeration, but the yellow space is what I am talking about. Archtops have a tendency to settle in under the string tension they have to bear. The top flattens, the center sags a bit and the outer ends of the feet naturally tend to lift. This tweak will help keep the feet down and snug against the top. If you overdo it, however, it will make the bridge top crack, as above. 

Don't underestimate the string tension!

The ideal situation is to leave a good bit of wood in the top (or saddle) of the bridge - it transmits sound better, and it won't sag.