Here are a few thoughts, some may not be possible or practical however.

Do your windows qualify as egress? Necessary for a bedroom.

Make part of the closet located at stair base as one for the playroom. Will qualify that space as a bedroom too.

Move the oil tank outdoors then, place your laundry in that space.

Have the bathroom at the base of the stairs. Out of the Family Room and closer to the bedroom(s). Enlarge it if possible - 4 x 5 will be really tight. Then access the Furnace/Laundry/Storage approximately where the bathroom shows now.

Double-wall the furnace to control noise in the Family Room. You may need a louvered door for combustion air.

Entertainment area? Room for a bar.

Good luck, looks like a nice layout with generous space.

I agree w everything fnmroberts said... I love planning spaces -- tho It's hard to answer this in too much more w/o knowing more of the constraints. Are you going to be tearing out walls? Where are the primary ducts to/from the furnace? Do you want to move ducts? Do you want to move gas lines? Do you want to move bathroom plumbing? This all severly impacts what you can do.

If yes you want to move any/everything, then I'd do like fnm said and move the bathroom over by the bedrooms, while making the family room wider. You probly have a beam going across somewhere in there too tho which might impact what you can do.

Move the bathroom over to next to the bedroom. i.e. between the fam and the bdrm, it'd be the door you see right in front of you when you walk down. Then make the Fam rm take up most of the right half, taking up about to the depth of the current bathroom of the unfinished space. Then you dont have to move your washer, dryer, and w/h hookups. Altho you would have to move your furnace (a huge deal).

If moving the furnace is not in the cards, then you are stuck w the L-shape concept that you don't like, and I agree, it's not at all ideal. Altho you can break it up into a TV / Couch wing and a Bar / Game wing... That's not really making the fam rm bigger (your original goal) you're just adding a bar nook.

Something like this. Alternatively if you dont like moving the bathroom you can leave it where it was, just making the new bathroom space in the pic part of the fam rm.

It all comes down to if you can move the furnace you have more options, but if not then you have to start w that corner walled off. You have a ton of space tho, wish I had that much room.

-mike