The top speed of the Mosquito was only part of the problem. The PR version maximum cruise speed was 358 MPH and it carried up to 850 gallons of fuelI'm going to make some long arguments and reasonings.
You're possibly right in that the He 219, while slightly faster than a Ju 88 with the same engine, would probably also be incapable of catching a Mosquito.
The problem is that the 650kmh/407mph Ju 88G/Ju338J with Jumo 213E is not going to catch a 715kmh/440mph Mosquito. In fact even a Mosquito NF probably couldn't catch a Pathfinder or Photo Reconnaissance Unit Mosquito.
The He 219 may have been the quickest opportunity around to make something that could at least match a Mosquito as the DB603L came in to use. I will argue that this engine would have allowed a 440mph He 219 even if the Do 335 was clearly much faster.
Luftwaffe programs were always messed up by either:
1 Cancelling them in order to get something better in the future eg Fw 187 to get Ta 154, He 219 to get Do 335. Ju 89/Do 19 to get He 177
2 Cancelling them to standardise eg He 219 versus Ju 388
2 Forcing them to use inferior engines in more plentiful supply thus converting a superior aircraft producing an uncompetitive aircraft not worth building at all. Fe 187.
3 Trying to convert them into "Multi Roll Combat Aircraft". Schnell(fast) bombers that were also forced to become dive bombers and often zerstoerers as well that then had to become night fighters. As a result these aircraft were too heavy and slow.
4 Heavy bombers that were also dive bombers. He 177 with 4 separate engines. They waited till 1942 to rescind this.
5 Giving up on concepts like long range single seat fighter entirely in order to force every specification into the suffocating zerstoerer concept.
The DB603L with 2400hp and two stage supercharger was starting to make a showing in 1945 on the Ta 152C.
With the DB603L engine the Do 335 was estimated to achieve 790km/h/490mph but our He 219 with this engine might be able to match a Mosquito at 710/440mph.
The He 219 existed and didn't need a complicated leading edge radar array like the Do 335. Both Ju 88/388 and He 219 aircraft could match the Mosquito in speed with the Jumo 222E/F. This engine was benching at 2800hp with B4+MW50 in 1940 and put on the production program but then removed when the standard was raised to 3000hp.
The problem is that the 650kmh/407mph Ju 88G/Ju338J with Jumo 213E is not going to catch a 715kmh/440mph Mosquito. In fact even a Mosquito NF probably couldn't catch a Pathfinder or Photo Reconnaissance Unit Mosquito.
So really nothing is available though the Me 262, Ar 234 and Do 335 are close.
And of course the British weren't standing still, There was still a little development potential in the Merlin they could have done such as 3 speed supercharger and with considerable work on the Mosquito the Griffon could be adapted. By June 1945 the Derwent V (scaled down Nene) was flying in modified Meteor III. The aircraft integrated into the Meteor III with eventually became known as the Meteor IV and was as fast as the Me 262 and could fly to 46000ft. It would be able to perform the Mosquitos Night Fighter role with a second cockpit, and its daylight reconnaissance role. It might be able to do pathfinding with an external bomb/marker load.
. If it were to intercept the same type at 25,000ft in the 16 minutes it takes to get to 25,000 ft its target has cruised 100 miles, but while climbing it is doing much less than 358 MPH. The Mosquito had a service ceiling near to 40,000, in practice vectoring an interception with prop aircraft is very difficult. The RAF had the same problem with Jabo raids at the end of the BoB.