Replace Broan 670 with new fan/light from bathroom
It is highly doubtful that it would be possible to simply place the guts of a new fan unit into the housing of an old fan, especially when it is a different manufacturer. In addition the fact that the new one has lighting in it means that there will be different wiring provisions inside the new housing for two circuits and your old housing only accommodated a single circuit.

The differing models are also highly likely to have differing size and type of fan blade assembly and air guides as well. Attempting to deconstruct both the old and new units to be able to swap parts just to save an old external housing might be possible but it is not something you are going to do reaching up into the ceiling. Instead you would have to have both units out on a workbench to perform the surgery. Such work would likely include breaking spot welds and needing to drill holes and use sheet metal screws to reassemble. But hey if you have it out on a workbench why not just mount the new one in the ceiling. 

It has been my experience that you can replace the fan from below (I've done it on flat roofed houses where there was no attic) but you should plan from the outset to remove the ceiling drywall back to the center of the next ceiling joist and make the cutout be large enough that you can work through it. You will need access to:


Disconnect the vent pipe from the old unit.
Shut off the power and remove the wiring connection from the old unit.
Demount the old unit from the side of the ceiling joist.
Mount the new unit.
Connect the vent pipe to the new unit.
String new wiring cable from the fan to the switch location with the added wires needed to deal with both a fan and light switch/dimmer. 
It has also been my experience that it takes at least one or two holes through the drywall to be able to route the new wiring cable and remove the old one.
Connect up the wires of the cable to the fan box following the manufacturer directions.
Cut a new piece of drywall to cover the hole in the ceiling and go around the new fan housing. It can be a good idea to lay flat pieces of wood along the top side of the unsupported edges of the existing drywall and secure in place using drywall screws through the drywall into the wood. This provides a support so that you can mount the new piece along as many edges as possible. 
Drywall mud, tape and refinish the ceiling as appropriate.


You did say you had an attic...even though access may be difficult it may still be less work overall to replace your fan from above even if the clearance to rafters is only a foot or so.