Car shaking only while accelerating, codes, P145C and P0497

Hi,

My car just recently began shaking when accelerating. It appears to be mostly in a limited speed range, usually 40-45 mph, and is most pronounced when driving up even slight hills.

The shaking does not remind me of an unbalanced wheel, which wouldn't apply here anyway because it occurs only when accelerating, not when coasting or maintaining speed.

The shaking doesn't seem to occur below or above that speed range, at least not noticeably. The shaking stops when the car shifts and the RPM's drop. Driving at that speed range, unless uphill, does not cause the shake as near as I can tell.

This started happening suddenly this week. A few weeks ago I had new spark plugs installed at recommended mileage. I do have a check engine light for two codes, P145C and P0497, which are emission related and seem to be due to a fault EVAP purge solenoid. This I've been living with for months under the impression it wouldn't affect anything, but now I'm wondering. There are no misfires or other codes are registering on the code reader (and a mechanic has used an expensive tool to verify my iPhone-based reader).

Reading online I've seen possible causes mentioned of bad CV joints, loose vacuum hose, throttle position sensor, bad motor or transmission mounts, torque converter, transmission, and on and on.

Don't know cars, but can't logic and some simple tests rule some of these out? For example, does the lack of codes strongly imply it isn't a misfire, transmission, or torque converter problem or don't those always show up as codes? Would a bad CV joint show symptoms always or only at certain times like that? The car accelerates fine through other speed ranges without symptoms, it just shows up at that 40-45 (maybe 50) zone.

Any help is appreciated!

John