TL;DR: According to the Domus Aurea drop data provided for Quetzmas, the increased gold currency efficiency from the Muscle Paradise node saves some AP over the Front Square node, resulting in a few extra boxes (minus the QP for reasons explained below) in exchange for a variable amount of QP.

SUPER TL;DR: DOING MUSCLE PARADISE INSTEAD OF FRONT SQUARE FOR GOLD CURRENCY IS LITERALLY EXTRA LOTTO BOXES (MINUS THE QP)

Important Considerations:

This method of squeezing out extra lotto boxes should NOT be used if the following scenarios apply to you:

1. You want hearts/fluids and don't need soaps.
2. You've already finished gold shop (duh).

Sample Scenario w/ Math:

Assumptions Made:

-Gold currency bonus is +1 (friend support CE).
-Lotto currency bonus is +6 (friend support MLB CE included).
-Total gold shop currency needed is 2200 (everything except for lotto CE and pieces/monuments).

Muscle Paradise Calculations:

The gold currency rate is 62.87 + (20.96 * X) drops/run, and each run requires 5 belts (2.5M QP).

Drops/run: 62.87 + 20.96 = 83.83
Number of runs: 2200 / 83.83 = 26.24 (round up to 27)
Number of belts needed: 27 * 5 = 135**
QP cost conversion of belts: 135 * 0.5 (500k QP/belt) = 67.5M QP

** Important note: this means that one would at least need to have 34 boxes first in order to obtain the belts necessary

Front Square Calculations:

The gold currency rate is 31.68 + (13.84 * X) drops/run.                                           The lotto currency rate is 34.73 + (13.16 * X) drops/run (here, X is assumed as +4; 4 lotto CEs are used with a friend gold CE).

Gold Drops/run: 31.68 + 13.84 = 45.52                                                                 Number of runs: 2200 / 45.52 = 48.33 (round up to 49)

Lotto Drops/run: 34.73 + (13.16 * 4) = 83.37                                                       Number of drops: 83.37 * 49 = 4281                                                                       Number of boxes: 4281 / 600 = ~7                                                                                   QP gained: 7 * 6.48 = 46.23M QP

Final Calculations:

The lotto currency rate for lotto node is 44.51 + (16.56 * X) drops/run.

Drops/run: 44.51 + 16.56 * 6 = 143.87
Number of drops: 143.87 * 49 = 7049.63
Number of boxes: 7049.63 / 600 = 11.74 (rounded down to 11)
QP per box: 11 * 6.48 = 71.28M QP

Thus, you've spent 42.45M QP (67.5 +46.23 - 71.28) worth of belts on Muscle Paradise to save 49 runs of Front Square. This means you've gained extra 4 boxes worth of mats, MP, exp, etc (minus the QP).

Link to Atlas Academy Sheets with live values : https://atlasacademy.io/data/