According to Wikipedia by
March 1944 Fi 103 V1s were produced in
350 hours (including 120 for the autopilot).
Figures from Anthony Kay's "German Gas Turbine and jet engine development 1933-1945"
for the BMW 109-003A-2 taking 600 man-hours out of a planned 500. These are actual German figures and conform with the production engineers Dr Fattners estimates of 500 man-hours per engine.
The Porche 109-005 of course had to produce about 50% less thrust and was required to have a total life of only 2 hours as opposed to a MTBO of 25 hours for the 003A2 (probably refurbished 4 times if no combat damage)
It's therefore not conceivable that the Porche 109-005 or simply 005 could be 50% x 50% less cost ie 25% as much (say 150 man hours) than the man rated BMW 003A2.
Noteworthy is that this doesn't include the cost of raw materials it such as sheet stock. Material is not expensive if steel but can be used but unless it includes nickel and chromium due to the high cost of mining and refining it. If the turbine inlet temperatures are kept below 650C the turbine can be made a 2 hours throwaway item of pure steal, this is what was planed for some of the German jet engines. Your turbojet is inefficient and big but its still better than a pulse jet.
If we assume the V1 cost 230 hours (excluding autopilot) and that 25% of this cost was the pulse jet (57.5 hours) then substituting the turbojet only adds 90 hours cost.
Out V1 now costs not 350 hours but 440 hours total and has both more accuracy and range. If we assume the electronics for guidance system (Ewald 2 also known as Ewald-Sauerkirsche added the same as the autopilot again (120 hours) we end up with a long range turbojet powered guided V1 for
560 hours compared to 350 hours for the short range unguided versions.
Some things are known of the 109-005.
It used a geared compressor to optimise both the compressor and gas turbine. Though this sounds fancy (geared compressors are absolute state of the art Pratt and Whitney tech) this is a small gearbox that could be cast and machined in one piece. It would considerably reduce project risk as matching the compressor to the turbine is simplified by adjusting the gear ratio. It was also intended to shed ice.
The BMW disposable turbojet was of a conventional design.
So yes a guided turbojet powered V1 was probably only 50% more expensive as a shorter ranged unguided one and even if it were twice the price it would be 'affordable'. If you say its twice as expensive I say its still cost effective.
Interestingly the Germans experimented with the idea of semi disposable aircraft that were pulse jet powered. The deposable 109-005 gave these projects, such as the Me 328 a new life.
The Ewald 2 guidance system worked by receiving a single pulse from the V1 missile whose differences in arrival times in 3 fixed ground stations allowed a position to be calculated. Now consider that Three carrier aircraft launch a missile each. At a certain point one of the missiles emits its location pulse which are received by all three aircraft and then instantly relayed to three ground stations. There is now enough information from the differences in arrival time to locate not only the position of each of three aircraft but the missile.
Hence air launched turbojet powered guided V1 allow for considerable potential in long range and reasonably accurate guidance.
The reason I know it works is because the US built the Loon and that means an independent set of highly competent military officers and engineers analysed it.
Figures from Anthony Kay's "German Gas Turbine and jet engine development 1933-1945" for the BMW 109-003A-2 taking 600 man-hours out of a planned 500.
German Production Costs
This is much less than a piston engine.
Breakdown is:
Machining 220
Sheet Metal Work 160
Starter Governor 60
Miscellaneous 100
Assembly 60
There are further breakdowns with the 66 turbine rotor blades requiring
only 10 hours.
Of course this doesn't cover the cost of refining and transporting metals and raw materials.
The time taken for the Jumo 004 was 700 manhours. (But remember cost drop as production is refined.
In both engines there was very little nickel, chromium or manganese. At most 6kg of each with nickel virtually eliminated to 200 grams in some versions. Nickel was in very short supply.
The website
Vorwort lists the manhours required for a BMW 801 as
"Durch eine Optimierung der Fertigung wurden die Preise für die Motoren immer weiter gesenkt. Der Preis einer BMW 801 Motoranlage lag 1940 bei 80700 RM und Ende 1942 nur noch bei 45000 RM. Davon entfielen 35600 RM auf den Motor und der Rest auf das Kommandogerät (3000 RM) und die Verkleidung des Motors (6400 RM). Die Anzahl der Fertigungsstunden betrug Ende 1942 etwa 16000 Stunden pro Motor."
Or in English
"The prices for the engines were continuously lowered by an optimization of manufacturing. The price of a BMW 801 engine was in 1940 80,700 RM and at the end of of 1942 only 45,000 RM. Of this 35,600 RM were allotted to the engine and the remainder to the control unit (3,000 RM) and the lining of the engine (6,400 RM). The number of manufacturing hours amounted to at the end of 1942 about 16,000 hours per engine."
I would assume that a V12 engine like the DB603 would be about the same.