Heartworms actually are mostly located in the pulmonary arteries, the blood vessels that take blood from the right side of the heart to the lungs to get oxygen. Their presence in these tubes interferes with the circulation in the lungs, and makes the arteries themselves inflamed. This can cause swelling, which narrows the opening in the artery, further interfering with this blood circulation.
Even when there are no worms in the heart yet, this difficulty in the lung blood vessels makes it more difficult for the heart to do its work. This causes excessive wear and tear on the heart.
Doxycycline inhibits a microorganism called Wohlbachia that benefits the heartworms (much as the "good" bacteria in our intestines help us). When the dog takes doxycycline, the heartworms become weaker and physically smaller. Thus, they cause less interference with the dog's circulation. Doxycycline is also a little bit of an anti-inflammatory medicine.
Prednisone is a form of cortisone, which is a potent anti-inflammatory medicine. If the worms are causing swelling of the blood vessels (making the opening smaller, and more difficult for the heart to work against), the prednisone can open things up again.
There is currently a severe shortage of Immiticide, the drug used to kill adult heartworms. Until it becomes available again, the American Heartworm Society is recommending that dogs be managed in the way that your veterinarian is recommending.
I think that your veterinarian's recommendations are very reasonable, considering your circumstances. If you have more questions, please take the time to let him/her know. Many times we think that we are great communicators. If nobody calls back, we just assume all their questions have been answered. If you have more questions, I'll bet that your veterinarian will be happy to discuss them with you.