You don't say how long each run is, but I guess they've got to average 200 feet each. That's way too long a run for 12v/12 gauge. I think you'd see serious voltage drop even if you did switch to 10 gauge wire. I'm not sure you're going to fix this problem within the budget you have in mind. Before you cross your fingers and buy something you're not sure about, do some more research. Here's an article to get you started... Here is a link that might be useful: The Fundamentals of a Successful Low-Voltage Lighting Design

The issue that quickly shows up with using NM for lov voltage wiring is the sometimes very high currents required by low voltage lighting. The wire size is based on current, with voltage playing no part (voltage determine insulation thickness). A 20 watt bulb in 120 V pulls ~0.167 amps. On 12 V a 20 W bulb pulls ~1.667 amps, and the lower voltage puts a premium on voltage drop. Dropping 1 V in a 120 V circuit is less than 0.83%, while in a 12 V circuit it is 8% and will result in noticeable color shifts (red tint) if a lower drop lights is nearby. To control voltage drops wire size may need to be increased evrn further (there are online tools that will compute voltage drop given current, wire size, and conductor length). Wire size directly affects box fill calculations and bending space. Larger conductors are often stranded to make working with them easier. The larger wires also require larger wire nuts, and may not even fit under screw heads on switches. I use small electronic 'transformers' (actually small power supplies) to power low voltage under-cabinet lights and avoid using a single large physical transformer. A 30 W power supply is less than 3 inches long x 2 inches wide and 1.5 inches thick *(most are closer to 1 inch thick). They are available for plug or hard wire connection and can use conventional 120 V dimmers. The 120 V wire can be as small as #14 (15 amp circuit) and is not hard to work with. The small power supplies can be mounted under the cabinets near the back with the lights near the front. The only complaint I have about the power supplies is they need a small strap to hold them in place (the single screw and double face tape fails pretty quickly).

Don't get halogen, they are way too hot. And don't get pucks, they will leave circles of light on your countertops, rather than provide even lighting. Xenon strips are a better choice for more even lighting on your countertop. I am linking a recent thread that will give you helpful information. Here is a link that might be useful: Thread about Xenon Undercab Lighting from Lowe's

If it is not staying tight, pretwist is your friend. And you might be using the wrong size nut. I disagree with ron on the pretwisting (again everyone has their own opinion on this). I have taken off various nuts not pretwisted and the wires are completely loose, or they arced so much that they were welded together and I couldn't get the nut off. When I take off a nut on my pretwisted connections they are still together tight. So the claim that pretwisting does little in the long run is wrong. I have read an entire thread on a different forum of people going back and forth on this so whatever works for you. I personally have had to redo a lot of junction boxes with loose connections done by someone else and have never had a problem with my connections. The connections of mine that I have undone were for later modifications and they were just as tight as ever after taking the nut off. One of the valid arguments against pretwisting is that when that is all you do all day it is extra wear on your wrist, which I agree with. If the nut alone could twist the wire and get it tight and keep it tight then I wouldn't pretwist, but I have not experienced that in the limited electrical work I have done.