Assuming the SM58 is the commonplace standard model that's low impedance (uses XLR-XLR cable and probably has "LowZ" written on it somewhere) I doubt there's an impedance mismatch unless you're trying to use an XLR-jack cable in which case you need an XLR-XLR. If youy use an impedance matching transformer to turn a LowZ mic into a high Z and plug it into an instrument/line level input you might well find you get even less gain than you already have. Instrument inputs usually have less gain than mic channels.
 
The Tri-capture doesn't have much gain at the mic preamp and the SM58 isn't really meant to be used at the kind of distance you're looking for. About half that is really the maximum. An SM57, which is basically the same capsule in a different shell, has difficulty with a guitar cab or brass instrument at 20cm. I use one live on a diatonic accordian and need it no more than 10 cm away from the instrument to get a strong enough signal at the mixer and believe me, you wouldn't want to try and sing louder than the accordion is at 8 inches (or a guitar cab). Live, singers like the SM58 because it is pretty feedback proof and by working in the range where lips almost contact out to around 10cm you can manipulate the bass response of the mic by simply moving it.
 
I'd suggest either getting the distance to the mic down using a boom stand or considering a more sensitive condensor mic or maybe a preamp to boost the mic to line level then run that into the Tri-capture.

The Taming of the Shure
http://www.recordingmag.com/resources/resourceDetail/330.html
Shure SM57 Impedance Modification
A simple gizmo makes a big difference
By Paul Stamler

That is a very well written article.

Cloudlifter? 
 
This might also be the case for one of those ART MP units - the "tube" preamp.  I forget the gain but it is likely to be greater than the Tri-capture.  It ain't great and the tube will go all pillowy if you drive it, but it is only $50.

As AT said, the distance is more likely the real issue IMO, since one of the biggest advantages of a dynamic mic is the reduction in the environmental input. Unless you have a powerful voice, 20cms isn't going to "cut it" to get the levels you are asking. A side note here is that with 24-bit recording, you don't need it "high" anyway as long as the S/N is good (this point depends on application).
 
A good mic stand with a locking boom may be a better path to pursue. Even watching popular pianists with powerful voices, their distance from the mic many times it actually touching it. Something to consider anyway.

I had a client who just was all over the place and often distorting on a standard LDC so I grabbed my Beta 58 and told him to stay right on it. I put a cheepo wind sock on it. I got a surprisingly good performance and actually liked the sound better than the LDC ( AT2020) for this person. Each singer may need a different mike. Beta 58's are worth using. Plain SM 58 are not what I'd ever use for recording. They have no clarity. 

Cactus Music
Plain SM 58 are not what I'd ever use for recording. They have no clarity. 

Read this article about impedance matching for sm 57/58 mics:
 
The Taming of the Shure
http://www.recordingmag.com/resources/resourceDetail/330.html
Shure SM57 Impedance Modification
A simple gizmo makes a big difference
By Paul Stamler
 
""The differences were clearly audible...  At 2k the sound was bright and ill-differentiated, almost like bursts of pure white noise, and quite unpleasant. At 500 ohms, however, it was like we’d plugged in a different microphone. While the sound was still brightish, it had much more detail, and the wash of hiss was replaced by the sheen characteristic of real cymbals.""

I've looked up the specs for the unit above:
Nominal Input level
Mic input: -60 to -30 dBu
Guitar input: -25 dBu
Line input: -10 dBu

Shure SM58
Sensitivity: –54.5 dBV/Pa (1.85 mV) 1Pa=94dBSPL

Thanks again guys. Learned a lot from your inputs. I'll try out the feasible options and see how it works out. And will update here so that it can help others in the future.
 
Regards,
Kane