The Miami Dolphins have the most rush attempts by a team with 48+ passing touchdowns in a season, with 484 carries in 1984.

most ((pass yards rush yards)/(pass attempts rush attempts)) by a team in a season with 48 (pass tds rush tds)
Interpreted as:
most ((pass yards rush yards)/(pass attempts rush attempts)) by a team in a season with 48 or more (pass tds rush tds)
1984Dolphins2013Broncos1961Oilers2007Patriots2020Packers2004Colts2011Packers2018Chiefs484461452451443427395387
TEAMSEASONGPRUSH ATTPASS YDSRUSH YDSPASS ATTPASS TDRUSH TDCMPPCTAVGYDS/GTD%INTINT%SCKSCKYRATE
Miami DolphinsMiami Dolphins1984164845,1461,918572491836764.29.0321.68.6183.114128108.5
Denver BroncosDenver Broncos2013164615,5721,873675551646168.38.3348.38.1101.520128114.4
Houston OilersHouston Oilers1961144524,5681,896498481525451.09.2326.39.6295.81417690.7
New England PatriotsNew England Patriots2007164514,8591,849586501740368.88.3303.78.591.521128116.0
Green Bay PackersGreen Bay Packers2020164434,2992,118526481637270.78.2268.79.151.021193121.5
Indianapolis ColtsIndianapolis Colts2004164274,7321,852527511035367.09.0295.89.7101.914109119.7
Green Bay PackersGreen Bay Packers2011163955,1611,558552511237668.19.3322.69.281.441237122.6
Kansas City ChiefsKansas City Chiefs2018163875,1261,855583501638566.08.8320.48.6122.126171113.8
StatMuse has team, season-level data for passing attempts, passing yards, rush attempts, and rushing yards going back to the 1932 season.