I haven't set up a car for down force, much less an F1, but mathematically, I don't believe that your supposition is correct.
DRS can't have a greater reduction of drag on a high down force car because there's only one element being removed from the equation and to a lesser degree. The fixed elements are still creating high amounts of drag, so the DRS element bears a lower percentage of the total down force created.
On a low down force set up, like Monza, the DRS element accounts for a higher relative amount of the down force, so when it's removed, the difference in drag should be greater.
The DRS is only allowed to move a fixed amount (50mm), so if the element is set up for higher down force, it will still provide more down force than it would in a low down force set up, because it's movement is still 50mm relative to it's original position (one being a high down force position, the other being a low down force position). Even if the element were a constant in the two set ups (as in the same original angle), DRS would still have a greater effect in a low down force scenario.
so hypothetical math. (assuming a 733kg F1 car with fluids, etc, etc, rounded to 800kg)
(high down force set up) 800kg of car + 3x downforce = a downward force of 3200kg
(low down force set up) 800kg of car + 2x downforce = a downward force of 2400kg
Assuming the DRS element is a constant and it adds 200kg to the downward force (I don't know the exact amount DRS adds), that force is a proportionally greater component the low down force set up, so the relative speed gain should be greater. (6% of the down force versus 8%)
For the DRS deployment to give greater gains in the high down force set up, the DRS would have to account for a greater percentage of the total down force.
Did I miss something?
Without being overly authoritative, and keeping in mind my limited expertise in aero knowledge as well, I think using downforce figures to illustrate this is not the best way. Yes downforce is related to drag, but they are not equal and downforce doesn't affect top speed (except for cases where the car lifts dangerously at speed, example CLR at Le Mans). Also a lot of the downforce produced is from the floor/diffuser, which contributes little to drag and needs to be taken out of the equation since DRS doesn't affect it. Secondly, a lot of the drag in open wheelers is from the exposed wheel/cockpit/suspension, which again will be constant no matter what wing setup you use. Even lowering the wings to minimum downforce is only going to reduce the drag by a small amount in the grand scheme of things.
Taking those factors into account, what we need to look into then is basically just the drag of the front + rear wing. According to wikipedia, the Cd of F1 is around 1.4. If we assume 50% of that is from the wheels/cockpit/suspension, then the front and rear wings produce about 0.7 of drag. Let's say they each contribute 0.35. Then let's say DRS when open reduces rear wing drag by 50% (eyeballing the size of the slot compared to the height of the rear wing roughly is half). Low downforce setup has roughly 75% of the drag of high downforce (middle ground between DRS open/closed).
Then hypothetical math:
HDF
DRS closed = F 0.35 + R 0.35 = 0.70 Cd
DRS open = F 0.35 + R 0.175 = 0.525 Cd
Difference = 0.175 Cd (25% from baseline)
LDF
DRS closed = F 0.26 + R 0.26 = 0.52 Cd
DRS open = F 0.26 + R 0.175 = 0.435 Cd
Difference = 0.085 Cd (16% from baseline)
Of course, this is all just back of paper calculations and Adrian Newey will probably laugh at it. But that's how things stand in my mind anyway.
BTW, I also did a test in Assetto Corsa. Using the SF70-H at a top speed test track mod with 3km long flat straight:
HDF - 305 kmh (DRS closed), 312 kmh (DRS open), difference 7 kmh
LDF - 335 kmh (DRS closed), 340 kmh (DRS open), difference 5 kmh
So not as dramatic difference as GTS, but LDF has smaller difference (as per my hypothesis).
Gearing can't be adjusted in AC unfortunately, but they both sit at roughly 12,000 rpm (HDF at 7th gear, LDF at 8th gear) at top speed so we can assume the car produces the same power. Also used manual full battery boost in both cases (the deployment profile doesn't give equal boost at 7th and 8th otherwise).