Your recipe will make a nice beer, but I'm afraid it won't be a Steam Beer....It's the use of these non base malts that allow us to vary styles of beer, along with the range of hops and yeast that we can use. A steam beer or California Common, needs to have the silky mouthfeel and fullness that the flaked barley, wheat and oats provide.
My clone attempt on Aussiehomebrewer called
Full Steam Ahead depends on these grains. In your instance, I would go with the LME and Crystal, cutting back the LME to around 2.5kg and do a partial / mini mash with a six pack esky and two stock pots from the kitchen...it's easy:
Trough Lolly's partial mash in the kitchen method!
Just 1/2 fill the mini esky, with 74C water that's been pre-heated in a stock pot on the stove (or boil the kettle and tip it in and add warm tap water to get to 74C). Gradually pour in a kilo of pilsener malt, 400g of flaked barley, 200g of flaked wheat and 100g of flaked oats, stirring gently as you go. You eventually want the mixture to have the consistency of soft porridge and a temp in the esky of around 66C - use the coffee kettle or cold water tap to adjust but it's not the end of the world if you're a few degrees either side of 66C. Cover the mash and let it sit for 60 mins, stirring every 15 minutes - ignore the inevitable temperature drop - most of the conversion will occur in the first 30 mins anyway.
As you near the end of the one hour mash, heat about 3L of water in the first stock pot to 70C. Place a colander over the second stock pot (which will be the kettle). Ladle grains into the colander from the mash esky and drizzle 300ml of hot sparge water over the grains allowing the sweet liquor to accumulate in the kettle. Eventually you should have collected around 4-5L of sweet liquor (remember we half filled the mash esky and heated up 3L of sparge water) and you can boil that liquor with half your hops in that pot and use the now empty hot water pot to boil up the LME and crystal with the other half of the hop bill.
Chill both pots in the sink / bath / swimming pool etc and you've got a batch ready for the California lager yeast....
It won't be long before you'll wonder what all the fuss is about and you'll be making all grain beers.
Cheers,
TL