Sound proofing HVAC ducts

First off, a reality check; not trying to discourage you, just trying to set some expectations here:

• First off, the actual pressures you're dealing with are very small. Absolute pressure is measured in Pascals; 1Pa = .0001psi. Your 80dB sound is inducing pressure changes of approximately .2Pa = .00002psi (that's two hundred-thousandths of a psi).
• Second, the percentage changes you need to make to these small pressures are very large. The Bel scale is logarithmic, based on a "reference" pressure. One Bel - 10dB - represents a tenfold increase in pressure. So, a 90% reduction in the pressure of your 80dB sound only reduces it to 70dB; to get the sound level below 10dB (you or I would call that "silence"; in laboratory conditions the threshold for human hearing is 0dB) would require reducing the pressure differential by 99.99999%.
• This level of isolation is possible but extremely cost-prohibitive in most applications; million-dollar recording/mixing studio spaces are built with lower levels of soundproofing than this. You normally see this level of isolation in medical and sound engineering research labs, where they literally build a room within a room, suspended on vibration-dampening struts, with a near-vacuum maintained between outer and inner walls of the chamber.

The upshot of all of this is that, no, a reduction in sound of 80dB is just not possible on a $1000 budget.

Now, all that said, don't lose heart. First, you seem to have much more ability to make changes to your rented space than the average apartment dweller would have (though I'd double-check your rental agreement; if you're required to return the space to its original condition - or pay damages - when you leave, think carefully about studding in a new wall).

Second, much smaller reductions in SPL can make a very big difference. Soundproofing that reduces an outside noise by 20dB makes the noise sound only a fourth as loud. This is easily doable in your budget (add some sound-insulating material such as mass-loaded vinyl between the existing wall and an extra sheet of drywall or wall covering), add a sound-insulating curtain or three, etc and you'll start hearing results pretty quickly. Two layers of mass-loaded vinyl will reduce most sounds above 125Hz by 18dB just by itself.

I would guess that modifying the duct work in a 1920s masonry construction home will be prohibitively destructive and involving removing or damaging irreplaceable trim that contributes to the building's character.

Mini split heat pumps:

An alternative, which will not be inexpensive but may be significantly less destructive, would be investigating installing a multi head mini split ac unit with one head in each bedroom. Such a unit costs perhaps $2500 to $5000 for the unit, installation extra and depends on the difficulty of install. If you live in a heating climate, especially one with cheap electricity in the winter or might install solar and have sunny winters, you should likely invest in the heat pump versions. Models are available that operate down to -13 F now (Mitsubishi M-Series) in single head. Supposedly multi-heads that operate that low are coming out this spring.

Advs:

Individual temperature control for each bedroom - Really high efficiency available for both heating and cooling - Avoid destruction of interior trim

Disads: - Potentially a lot of $$$ - Still a newer technology in the US (used all over Europe and Japan). If you plan to sell soon, recovering your investment at resale could be a challenge - Some people hate the look.

Other than minisplits:

Air leakage:

I'd suggest you have a blower door test performed. All the insulation in the world doesn't matter if you are changing over the air in the house too quickly. If you didn't air seal the attic before filling it with cellulose, you could have this problem. An infrared gun on a cold night can help show these leaks too. Insulation installers will say things like seals in air but cellulose, fiberglass insulation, and mineral wool insulation are actually very air permeable. If you find that is the problem, you could move insulation out of the way in the attic to use canned foam (get a commercial gun, much nicer job to do than with home depot cans). If you can't move the insulation, you could install a vapor permeable sheet membrane like Tyvek or a smart vapor retarder like IntelloPlus on top of the insulation to block air movement. Do not use a vapor impermeable barrier like black plastic or visqueen (clear plastic); you could trap moisture and cause a mold problem. Attic access hatches are also causes of large volume air leaks. There are special hatch covers you can buy or build to address this problem.

Duct work in unconditioned space:

Do you have any ducts in unconditioned (uninsulated) space like an open crawl space or an unconditioned attic? If so, you could be losing huge amounts of heat to the crawl space or attic. If your ducts are older, they likely aren't air tight either. You could use specialized foil tape or duct mastic to seal the joints and you could insulate this duct work, though it won't be fun work. If your ducts are really leaky, you could get big gains in system performance from this work.

Humidity control:

Have you measured your humidity when your system is running? If your humidity is high in the winter or summer, you will feel colder or hotter. Your humidity could be high in the house for many reasons (improper shower venting) but dirt crawl spaces are a big source in the summer (not in the winter so much). Seal off the dirt crawl space to eliminate humidity, mold spores, radon, etc. from getting in the house. A radon membrane company, in areas with radon, might be a cost effective contractor to use.