There are slow-rise polyurethane foams that vary from ~R13 to ~ R20 (depending on density) that can do the job, but it's wicked expensive & slow, with a high risk of blowout. The higher the density, the higher the risk, but with half-inch gypsum the risk is still signficant ieven with the low-density stuff.
With the lower density stuff the primary advantage would be the reduction of air-infiltration, since the R value would not change appreciably, but air-tightness is often achievable by other means. See if you can't find an insulation company that specializes in air-sealing, that will blower-door test/remediate/re-test to verify that they've made a dent in the problem.
In some instances it's possible & worthwhile to blow cellulose into the cavity over the batts, which will significantly reduce the air movement within & around the fiberglass and fill all voids. You end up with about the same steady-stae R-value, but reduce the infiltration & convection losses by 90%+, and adds significant thermal mass to the walls, which reduces the peak AC load by inserting a time-delay in the heat transfer through the walls. The effect on comfort is good, but the effect on the AC bill is most profound during the shoulder seasons, somewhat less so during the mid-summer, but it can mean an 8-15% % annual reduction in annual cooling load. It's easiest/cleanest in an occupied house to do it drilling holes from the exterior, but if it's brick or stone cladding it'll have to be done from the interior, which takes a bit more time.
Cellulose or slow-rise foam can be spot-retrofitted into known gaps in the insulation. If you have some known hot-spots, particular stud-bays that are measurably warmer on the interior than adjacent areas spot remediation can be very cost-effective. Better contractors would use thermal imaging cameras as well as other methods to find & fix all the thin-spots/gaps, etc. Air-sealing contractors are usually also in the spot-remediation biz.
If the attic is fiberglass batting at anything less than R38, an overblow of 3-8" cellulose can dramatically improve it's performance as well. Heat radiating in from the roof deck penetrates a few inches into the fiberglass, making the temp an inch or two into the fiberglass significantly hotter than the attic air (!), which means the remaining depth of fiberglass is fighting a higher temperature difference with less total R-value. With cellulose the radiant penetration into the fiber is nil, and the warmest temperature of the fiber layer is then the top surface, which tracks relatively close to attic air temp. Blown insulation also fills all gaps & voids, and it's the thin-spots that end up contributing the bulk of the heat transfer. Air sealing the attic floor/conditioned-space ceiling interface would come first though. If your AC ducts & air handler are in the attic there's often payback in insulating the roof deck and sealing the attic (instead of or in addition to upgrading the attic floor).
If this house has a basement or crawlspace, foam-sealing & insulating the foundation sill & band joist as well as the attic can be huge. The "stack effect" tends to pull air out at the top of the structure, pulling air in at the bottom. If you seal the top AND the bottom, even if the floors in-between are somewhat leaky, the continuous infiltration drive has been reduced by well over half. If it's a ventilated crawlspace, sealing it up properly with ground vapor retarders & rigid-board or spray foam on the foundation walls earth-couples the structure, which can also significantly reduce the AC load, since you're now dealing with 70F dirt & 75F air vs. 85-90F air under the floor when its 100F outside.
If you're up for a major upgrade without gutting the interior, stripping the siding "dense-packing" cellulose from the exterior, and applying 1-2" of polyisocyanurate ("iso") rigid board (taping the seams with FSK tape, and foam-sealing the edges to make it air-tight) under the new siding can double the R value of the walls with far better bang/buck than a slow-rise foam retrofit. But it's a significant cash commitment.
In order of cost-effectiveness it typically (but not always) runs:
1. air-sealing is usually by far the most cost-effective
2: attic insulation
3: spot-insulating walls
4: foundation insulation
5: insulating sheathing (but never re-side a 2x4 framed house without doing this, since it would be most cost-effective at the point you're re-siding.)
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