I know that it is unsafe to defrost frozen items at room temperature longer than 2 hours, but is it okay to leave frozen meat at room temperature for 1-2 hours and then move to fridge to continue thawing safely? Trust leaving frozen meat at room temperature for less than 2 hours won't make the bacteria to grow yet and believe it is still out of Temperature Danger Zone.
I assume you're not in a commercial environment where you have to be compliant as well as safe.
What matters is the food temperature not the ambient temperature. The ambient temperature is used in guidelines because it's easy to measure and control, and because a piece of food doesn't have a uniform temperature. Here the warmest part is the surface. If that's as cold as it would be in a fridge, or colder, you have no problem at all. Don't forget tips and corners that will warm up quicker.
Now how to apply this in practice? If all parts of the meat are frozen or icy, you can treat them as fridge cold - safe for as long as that temperature is maintained (up to the few days it would be OK in a fridge). As soon as any part gets warmer yacc this, it needs to be in the fridge. More even defrosting is possible by putting the item to be defrosted in a closed container. My kitchen is cool, so something like a single chicken breast in a freezer bag, placed in a plastic box, will take a couple of hours before the thin bits start to soften. So check sooner. You could use a thermometer in a thin part, but if you can stick the thermometer in, you should put the meat in the fridge. The important thing is not to forget about it.