$300 is tough at least you have a long action, your best bet would be a Bell & Carlson Medalist. It'll probably take some fitting to get the barreled action into the stock properly, and I'd recommend bedding it even though it has the bedding block. The B&C is a decent stock for the money and I wish they'd offer the Medalist for the short action Savage, but I haven't ever had one that didn't require fitting. It really depends on what Savage rifle you have, is it stagger or centerfeed, top or bottom bolt release, and detachable or blind magazine. The only thing that hasn't changed in all generations of the 110/111 action is the screw spacing, that's why you have better options for a sporter style stock than if you had a short action. If it is bottom bolt release or detachable magazine the Medalist probably isn't the stock for you.

If you aren't opposed to laminated wood stocks, Stocky's Stocks and Boyd's Gunstocks both fit in your budget and might require fitting. I haven't used either stocks on a rifle so I don't know how drop in they are, and I'd still bed them.

If you want a true drop in stock, then you're better off putting the extra money into a McMillan or Manners stock. You could also talk to Kevin Rayhill at Stockade Gunstocks for a money saver stock that you'll have to finish for under $300. However, if McMillan or Manners wait times have you turned off I've heard it takes Kevin even longer to build a stock. I imagine Kevin's stocks are pretty much drop in as he specializes in Savage rifles, but I've never used one either.