If I'm reading your question right, this is a crazy idea and I love crazy ideas.
Our Solar system poses a significant problem for colonisation insofar
that the rocky planets are predominantly on the... small scale; at
least as far as mass is concerned (Earth is the exception rather than
Size is important, cause you want a magnetic field, requires a solid/liquid inner core (less likely if the planet is too small), you want the planet to retain it's atmosphere (again, size helps - gravity being stronger), and you probably want plate tectonics (heat in the core is important there too) and you need the right temperature, but presumably if we can move enough mass to build a 2nd earth, we can move that mass as well.
However, there are many rocky planets, dwarf planets, moons, and
asteroids scattered throughout the system. Excluding the severe
logistical difficulties in generating such giant impact events in the
first place, are there theoretical means by which the masses of
different bodies can be combined, rather than their collisions simply
shearing vast amounts of debris off the larger body?
When you're talking about moving millions, billions and even trillions of tons, on objects that orbit the sun at many thousands of miles per hour, that's no easy trick, add to that, most of these objects are very far apart, so, as you say, logistical difficulties do exist.
By creating an atmosphere around the object, that will buffer to some extent any debris fly off. Glancing blows vs direct hits can help too and lower velocity impact, such as starting from mostly stable Trojan points might help.
Back in the early stages of the Solar system when the planets where
hot and less solid, such combinations seem to have been a real
possibility. Is it still hypothetically possible in a mature system?
Another problem that perhaps you haven't though of is the mass of all the stuff out there might not be as much as you think.
The total mass of the entire asteroid belt, including dwarf planet Ceres is about 4% of the mass of our moon. (Source). The mass of Jupiter's Trojans might be around that much as well (I read that somewhere).
The mass of all Kuiper belt objects might be significantly larger than that, but those objects are more icy, less rocky, not as good for building a rocky planet and enormously spread out.
Even the mass of all moons wouldn't be enough. Ganymede is larger than Mercury, but less than half it's mass, all the moons together would give you a bit more than the mass of Mars, and many of the larger moons are far out in the solar system and have more water, less dense elements. Pull too many moons together and you'll have a planet covered with oceans, which might not be all bad, but it's probobly not what you're going for.
So, if you really want to build another Earth like planet with objects in our solar system, you'd probobly have to combine Venus, Mars and Mercury (and maybe Europa for water). Those 3 planets combined would have a mass almost equal to the Earth. There's probobly enough Iron in there to create the desired Iron core, once the planet after the heat of smashing together cooled enough to have a solid metal center and a liquid outer metal core. Mars has a lower Iron ratio but Mercury has a lot of Iron.
Once they smash into each other, the newly formed planet would need a long time to cool, likely tens of millions of years or so. But you might be able to build an earth that way. I don't believe you can build an earth out of dwarf planets, moons and asteroids though. There's simply not enough material.