You simply aren't going to get what you want without going to a lot of expense. At 176mm you would need to buy something like 190 x 44mm (ex-8 x 2in) structural softwood (e.g C16) and have it machined to size, then rebated and an intumescent groove routed in the rebate of the casing profile. You'd probably need to have the housing joint in the head cut for you as well unless you are happy doing that with a portable circular saw and chisels or a router. Even then, with those dimensions I think you'd need to get the timber and install it really quickly after doing the machining to minimise the natural tendency of the timber to cup or warp (as a result of the of the relief of any internal stresses caused by the machining)
There is anither, easier and cheaper way to approach this, namely starting with a
standard rebated fire door casing kit like the 110mm wide kit I illustrate below (see note below about terminology) of this sort of section:
you machine a rebate onto the inside edge of the legs and head using a router, portable saw or possibly even a power planer (so long as it will allow you 8 to 10mm depth of cut). You then take some 22mm thick planed stock, saw it to the required width (plus the depth of the rebate) and rebate one edge of that to match, fir two legs and a head. This is called a
lining:
The two pieces are joined to the made-up door casing kit by glueing and skew nailing from the rear to form a single, wider casing of the desired width. The "leg extensions" can simply be butt-jointed and nailed or screwed to the "head extension", although a housed joint in the header is neater (albeit slightly more difficult to perform):
In order to make a less noticeable joint it is best to chamfer the mating edges of the two components where they abut, thus:
as this allows you to either flush fill the V-groove with 2-pack filler or alternatively to "wipe" a blob of flexible filler down the joint before decorating to create a shallow "rounded" joint which is relatively inconspicuous once decorated:
It is also possible to make-up this type of joint with a tongue and groove as opposed to a rebate if you have access to an appropriate router (probably 1/2in) and an appropriate size grooving (or better still tongue & groove) router cutter set:
whilst a butt joint with biscuits is another way to produce the joints
BTW a traditional approach to the joint is rather than hiding it, instead make a feature out of it by adding a bead profile:
Note: In order to get some clarity in terminology, this is what I was taught was the terminology and what I have used throughout my working life: a door
frame is generally thicker stock at least 40mm thick and designed for use on exterior doors
without any architraves; a door
casing is a rebated frame
designed to carry an architrave (in many, but not all, instances) for interior doors with a thickness of about 32mm; a door
lining is basically a flat frame where the lining is installed in the opening, the door swung and a stop lath is fixed to the flat face afterwards to limit the swing inwards of the door. the term lining is also used for extensions to casingscir door linings as illustrated above. Linings are generally not considered suitable for use in fire door installations as the seal between the planted on stop and the lining often has dubious fire resistance properties