At one time I owned a 20" bbl. m7 in 7-08... I shot a good bit of 140 sierra through it with h414 pushing- around 2750fps. I also used 120 sierra with rl15 pushing at nearly 3,000fps, but that pill proved rather soft for deer. If you want to use a 120 I suggest nosler; I hear the bt will hold up to deer hits.
Wife took her Tikka T3 Lite w/ 20" bbl. to Africa in 2013.
Kudu, Zebra, Blesbok, Impala, Gemsbok, Springbok, all one shot kills out to about 180yds. None went farther than 70 yds. or so.
140g Nosler Accubond. 2650fps w/ Varget. Sub moa at 200 yds.
PH begged me to "gift" the rifle to him as a tip. NOPE....gave him $1400 instead!