A far less expensive option would be to build a rifle using a Mauser or Springfield action which has a stripper clip guide.
Another possibility is the repro 20-rd mag for 98 Mausers (Sarco, Numrich).  As it was designed for stripper clip feed, it's not readily detachable.  And it would have to be modified for .308.

.308 Lee enfield?

Last I heard, Steyr was relocating their production facilities, and spare parts for some, at least, of their rifles were none too easy to get.
This may be old/incorrect news, but I'd carefully look into parts/service/warranty availability issues before I plunked down for a nice Steyr.  
IIRC, one member was searching high and low for a critical, unique screw for his Steyr.  It's been months that the rifle has been unuseable.
Again, I may be misinformed, and all this a thing of the past or an error on my part, but DO please investigate first.  FWIW.

We can make you one with just a drop in stock.
Here is a pic of mine. All you need is a Simple Rem 700 ADL (Their cheapest model to start with)

This is the Accuracy International Stock. It is a drop in unit that you can install. It comes with One 5 round mag. 10 round mags are readily available for only $89.95. Mine will shoot 5 shot groups in the Mid Ones. (Pencil eraser sized)
This is the best kept secret on the planet.
We have this stock on sale right now for $539.95 delivered price. Comes with one mag and needs no bedding.

The LONG awaited Long Action Stock (AICS) for the Rem 700, 300 Win Mag and .338 Lapua mag is finally here.
Available right now for immediate delivery.

$624.99 Delivered price in the CONUS.

Please Specify the 300 Win Mag or .338 Lapua Magazine

Available in Black or Green

Fixed Cheek Piece

Comes with 1-5 round mag (.338 or 300 WM)


Extra mags also available


.338 Lapua $64.95

.300 Win Mag $56.95


Also Available: .308 Short Action Stocks


Stage 1 $539.95 Delivered Price

Stage II $789.95 Delivered Price (With Adj Cheekpiece & Folding Stock)

Black or Green available. Comes with One-5 Round mag.

Available for immediate Shipping.

478.994.4560


Hurry, these won't last long. They have been on order for over 2 years and the demand will be very high.


www.georgiaprecision.com

Quoted: Hey RAF, what kind of work is involved in building a decent stripper clip fed gun like you described above? Would this involve buying an old C&R gun, and putting a new barrel/stock on it?

Pretty much, although you may have to do a little mag well, follower, and spring work since the new cartridge (.308) is probably shorter than the original chambering.  Maybe a new bolt, too, but not a big deal, since you probably will want a turned-down bolt handle instead of the original straight one.  Main thing is that the bolt accepts the .308 case head proprly.  Most old timer gunsmiths ought to have done the mag well work, it's not that involved: shorter follower, shorter (fore-and-aft) spring, and spacer brazed/welded to front to magazine to prevent cartridges from sliding forward.  Not rocket science, and all done many times before.
In fact, some rifles have been converted to 7.62 NATO by Arsenals.  The Spanish FR-8 Mauser and the Chilean Modelo 1912 Mauser (Steyr mfr!) were both so converted.
Now, this is important!  DO NOT use any Mauser receiver other than a 98 series to fire the 7.62 NATO, abd especially the commercial .308.  Anything earlier, like the 96 Mauser action used in, say, the Spanish FR-7 Mauser, is not rated as strong enough,  The late-model Springfields, are good to go.  I wouldn't hack up a really nice one, though.
As for scoping, take a look at the Scout set-ups here:www.ashleyoutdoors.com/.  Nice stuff, and back-up iron sights as well.  I've seen people with Scout rifles hit thrown clay birds, with practice.
IM me if you have any more Q's.