Here's an inexpensive amplifier kit you could build that would take you to the 35 watt level. That's about an S-unit stronger than what you have now:
You will need to reduce the power from your 10 watt rig into this amp. You can simply turn the power down on the Kenwood, or, a much better idea would be to build a 6 dB pad into the input of this amplifer, so the full output of the Kenwood doesn't overdrive the amp. If you overdrive the amp, the results will be distorted garbage.
In general, the CB amplifiers are junk. Oh, they may work, but since they're 100% illegal anyway, why do you think the makers might be inclined to spend the extra money to make sure that it has a clean output? Why? With a lot of work, you might be able to make it work, but it depends on how bad it is to start with.
K9ZMD's comments about your antenna are correct. The Antron is designed to work the higher ham bands - 17, 15, 12, and 10 meters. But on 20, 40, 80, etc.., it's going to present a very high SWR and it's also too short physically to work well. The high SWR means that a lot of your power is being wasted as heat in the coax. The short size means that it's less efficient than a full sized antenna. I would wager that you're radiating less than 1 watt for 10 in .
A 40 meter dipole is 66' feet long. Let's assume a reasonable SWR. You would now be radiating 10 watts. It will still be a challenge to make contacts on 40 meters, but you certainly should be able to make some, particularly in the daytime with a dipole. When 15 is open, you should be able to work North America about as easily as somebody running 100 watts.
If you simply can't do a horizontal dipole, look into larger verticals on the ground with lots of radials or on the roof with a few tuned radials.
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