Dear @Stijn_Muylle,
Just some brainstrorming:
With the method decribed in the post, it should be possible, the only change should be that the days will be monitored, instead of the month.
And then you could compare the start day to end day with the actual workout period and in case there is a difference the streak has to start again.
On your way creating, for sure you will face some challanges, but the community will be glad to support you.
Success, 
//JP