First of all, apologies for what comes ... (also this assumes Level 5 and below, when one FR replacement is required, not 2)
Until now I have bought fully into the reduction to 13 players following YC and subsequent injury. But ... this actually penalises the team that had an additional FR, who unfortunately then gets injured. If there was no replacement FR, the penalised team would play 10 minutes uncontested scrums with 14v15 players; then return to 15v15 with contested scrums. Because they had the additional FR, the intent is to play contested scrums with 14v15 players for 10 minutes. They manage to do so for, say, 4 minutes; then the injury means that they are in the same position as a team that didn't have this additional FR. Why should they be put in a worse position - uncontested scrums for 6 minutes with only 13v15 players? They have fulfilled the minimum requirement of one replacement FR, so should only be penalised because of the YC.
Otherwise, are we expecting that, having gone to uncontested scrums 14v14 for the rest of the match for an injury, every subsequent time that one of the remaining 2 FR is injured - by definition there is no FR replacement - then the team cannot replace that player with someone else from the bench, eventually resulting in 12v15? (I'm assuming that there still are fit non-FR players on the bench).
Logically, there are only 2 states of the scrum - contested or non-contested. It cannot go 'more uncontested'. Therefore, assuming all other things equal and at least one replacement FR available for any position, the match is either played 15v15 contested scrums, or 14v15 uncontested scrums, no matter how many FR may be injured. (Obviously not relevant for more than one concurrent YC/RC).