For total passing yards it's as follows:

2019 SDSU- Wilson had 316
2019 UMASS- Wilson/Critchlow had 308 (Wilson only had 293, so this only counts if you want team yards)
2019 Liberty- Romney/Simon had 306 (Romney only had 262 but Simon had one pass for 44 yards)
2019 USU- Hall/Romney/Simon had 418 yards (Hall had 214, Romney had 191, Simon had 13)
2019 Toledo- Wilson had 315
(Hall/Wilson missed 300 by one yard against USC)
2018 WMU- Wilson had 317
2018 USU- Mangum/Wilson had 322 (270 for Mangum, 52 for Wilson)
2017 SJSU- Mangum/Critchlow had 332 (283 for Mangum, 49 for Critchlow)
2017 ECU- Mangum had 319
2016 SUU- Hill had 320
2015 Utah- Mangum had 315

That's the point where there are 11 300-yard games, but 5 of those involve multiple QBs. If you want 300 yards by just the starting QB then we have to keep going.

2015 Fresno- Mangum had 336
2015 Mizzou- Mangum had 332
2015 UCONN- Mangum had 365
2015 BSU- Mangum had 309
2014 Memphis- Stewart had 348

So if you want 11 300-yard games from just the starting QB, then you have to go back to the 2014 Miami Beach bowl. If you want just 300 yards for the team then you only have to go back to 2015 Vegas Bowl.