Even without the same dire situation (albeit more focused use for offensive weapons) early war, I wonder if similar logic could have swayed more favor towards the Fw 187 pre/early war if proposed as a single-seat high speed fighter-bomber.
I think that the problem there is that the fighter-bomber concept, as in modifying a fighter to carry bombs to operate in what we would no call close air support or battlefield interdiction simply didn't exist in the mid 1930s. That's not to say that some adventurous types hadn't lobbed small bombs from the cockpits of their fighters in WW1, but this was developed into the dive bomber (almost every German bomber) or light bomber (Hawker Hart, ideal for cheaply and effectively bringing recalcitrant tribesmen into line, unfortunately the Fairey Battle couldn't do the same to the Germans). These were not fighters.
The first Bf 110s with bomb racks were not delivered by Messerschmitt until June 1940. 13 of these aircraft went to 1. and 2./Erprobungsgruppe 210. 3 Staffel got Bf 109 E Jabos at the same time. The British adapted the Whirlwind and Hurricane as fighter bombers a year or so later. All fighter bombers were an expedient rather than a design, forced on the various air forces by a tactical requirement their existing types did not fulfil.
The means to operate such aircraft effectively and the development of the command and control systems needed didn't really start until the British really adopted the fighter bomber in the Desert Air Force in 1942.
The Germans were just as attached to their 'Zerstorer' idea, though they did modify it from time to time, as they were to their obsession for dive bombing. Proposing the Fw 187 as a high speed fighter bomber, something like the British Whirlwind, is not something I think the RLM would have been interested in, nor would it have occurred to Focke-Wulf. The Fw 187s best bet was as an out and out fighter, but that was lost when the RLM wanted a two seat 'zerstorer' version.
As for the engines, the Bf 110 didn't start life with DB engines, the Bf 110 B-1 was the first to reach operational units, powered by a couple of Jumo 210 Gs. so I doubt any Fw 187 would have been better prioritised. The DB 601 A powered Bf 110 C was to be built from January 1939, a total of 990 by March 1940, according to Production Plan 8. Like all RLM plans this was never realised, though Zerstorer units did have the Bf 110 C by the beginning of the war.
The Jumo powered Bf 110 B was supposedly withdrawn to training schools in July 1939, though 27 Bf 110 Bs were still on the Luftwaffe's front line inventory as late as 31st August 1939, almost on the eve of war.
Going off at a slight tangent, I'm not sure that the Bf 109 'Jabos' were really used in what we would consider a fighter bomber role in 1940 at all. For reasons unrelated to this thread, I have been looking at the three attacks on London on 15th October 1940, all carried out by Bf 109s. The attackers approached at altitudes estimated at between 26,000 and 33, 000ft. The dropped their bombs from 18,000 to 20,000ft. The bombing was so inaccurate that British reports for the three raids could only assume the actual targets. The first spread bombs in the area around Waterloo and Vauxhaull, Waterloo station was assumed to have been the target though it was not hit. The British could not work out the targets of the second and third raids, bombs falling in the 'area around Tower Bridge' and then 'the Southwark area'.
The Bf 110s of Erprobungkommando 210 did carry out successful low level attacks, particularly on Fighter Command airfields, which look far more like what we would expect fighter bombers to do.
Cheers
Steve