Oh my gosh with the Polly Pockets!!
My daughter is the same age. Also the Littlest Pet Shops and Playmobile figures but really, whichever toy it is has little to do with it it's just the beg beg begging to play dolls with me dawn to dusk.
It's so NOT fun.
And yes, I work very hard to organize all kinds of other fun trips, crafts, arts, lessons, outings...which she does enjoy. But...Polly!!!
It's just the right-now attention need thing.
For the summer, we had a brainstorming session and struck a deal, which is basically a structure that says 'I recognize she needs this one-on-one role-playing playtime and I will do my damnedest to help her with this or die trying

; and she 'recognizes the need for the day to Move.On. already and needs to cooperate and do other things along with me and be helpful and have a decent attitude and play by herself while I work, too.' We wrote it all down together, very dramatic.

But, it's helped. I pledged to her a minimum of 60 minutes of PP playtime
given that the day was flowing and other things were getting done with out significant conflict.
It's working decently, I'd give us a B. And we are getting our errands/enough other activities to satisfy me/enough alone time/clean house/you know what I mean done. [I try to take a book into the PP time with me and not make it too obvious that I'm skimming it (sometimes my Polly's 'read with me'...she doesn't buy it

)]
I have more in the past and still do nudge the Polly roleplaying to homeschooly type directions. It 'works' but it is backfires some by not satisfying that 'itch' that she's scratching with the PP games...we're more efficient learning without the PP and more efficient playing PP without the superimposed 'learning' and it ends up being less productive all around. Plus, it is much easier for her to be excited and engaged in other activities when she's gotten her little PP cup filled

An exception to this is that I do stage plays with my PPs and encourage her to do the same, but that's as much for my own entertainment as anything else. It is one of the more worthwhile PP activities IMHO. Since the PP play is usually roleplaying families, all on her own she often has her parent PP give lessons (especially math lessons for whatever reason) to her child PPs. So we have that going for us, too.
That's a long answer (you'll have to forgive me, I'm avoiding playing Polly Pocket

) but all that to say, I do feel we've achieved at least an 80% at the same goal you stated, to have an organic/flexible/loose but productive, motivating flow to the day. I have a box system for myself (DD is only peripherally aware of it) that I use to be sure I'm hitting all the areas in her HS that I want to. And I think I go to bed feeling like we got somewhere and she goes to bed without feeling like she got dragged through the day and what she enjoys was ignored.
On the TV: that has been an issue in the past but for now we have a nice balance with it. If your daughter is like mine, I'm willing to bet that if you can get some balance with the one-on-one playing, the TV will recede back into the manageable background. Or it may not, but if my house looked like what you describe (and it has before, definitely) I'd try to work a deal on the playing first and then address the TV if it was still an issue.