umami - yes to the suggested soy, mushrooms, bisto, wine - all good shouts. Anchovy?
Teaspoon of vinegar could go a long way.
I would caramelise the mirepoix first very well, and do the meat separately very very well.
Gets rid of the celery soap. I also use celery salt sometimes instead for the flavour.
Celeriac is the work of the devil unless covered in mayonnaise.
I find I throw away very little if anything at all. I've become very good at making decent meals with a few ingredients (iron chef!). I think it's from learning about what (flavours) goes with what and having a good store of cans and dry ingredients to fall back on - lentils, grains, pasta, rice. This may help http://www.flavourthesaurus.com/ also I've cooked most of my adult life with Stephanie Alexander and the Silver Spoon - good reference books.
I'm a big fan of Lock & Lock plastic tubs which go into dishwasher well (the sistema ones don't) and the heavy duty snap-lock soup bags