Terminologically, the span would be the distance between the supports on either side. If the beam is in the middle, then that would be 10 ft or less, and I'd suggest getting an exact measurement from face of support to face of support (length of the portion of the bottom of the joist you can see).
Is there no way to raise the drain even more, so that you can go through a drilled hole? For the US building code, the allowable hole size is 1/3 the joist height, but the hole has to be at least 2" clear from the top and bottom (so on a 7.25" high joist, the middle 3.25" can have a hole up to 7.25/3 inches in diameter). I vaguely recall that the Canadian building code might use D/4 instead of D/3, in which case this wouldn't work (7.25/4 < 1.9).
As for notching, I'd suggest checking your building code's prescriptive span table, and determine if there's a grade and species of wood 2x6 where the allowable span exceeds the span you have (depends on the joists spacing as well). Then you could sister the 2x8 along the full length of the span (for good measure). The question is what nailing pattern to use for sistering, you could check you building code to see if it specifies a nailing pattern for doubled joists (like trimmer joists on a floor opening). The 2x6 would probably end up with a 1/4" notch, but that's negligible as long as it's not right next to a large knot.
In theory a steel strap attached to the bottom of the joists over the notch would restore its capacity, but designing the strap size and fastener size and pattern would require an engineer. And installing the strap so that it doesn't have any slack would be challenging.
Cheers, Wayne