The output voltage will be limited to between 21V and 22.5V depending on the current draw, temperature and voltage regulation requirements.
And the lower limit will be something like 2V.
When the output voltage is set very low the output current will be reduced due to the LM317's safe area protection (the current limit typically reduces when the voltage across it is >15V) and the fact that it might be overheating anyway.
You need plenty of cooling, and might consider a high power cousin.
Have you considered hacking the SMPs to give a variable output voltage? That's what I would do. Mose SMPSes use the TL431 to regulate the output voltage, which can be tweaked by replacing a fixed resistor with a pot. It should be possible to reduce the voltage down to 4V and up to over 24V, although be careful not to increase the voltage too much because some of the components on the secondary side won't be able to handle higher voltages, you should be fine to 30V though.
I would be worried about the design (controller, magnetics) being able to cope with the very different duty cycle.
Something else to consider is that many SMPS's have a specified minimum load for proper regulation, depending on power, this might be something like 100mA (that's one huge power LED). What will the SMPS do if the output of the LM317 is shot circuited? The initial short circuit current is something like 2.5A (should be a graph in the datasheet), will the SMPS survive that? Not all SMPS designs are that stable in all circumstances, since they were not developed as lab supply. There is at least one documented case of someone who build a lab supply with an LM317/78xx and an SMPS, and the SMPS committed suicide, blew up the linear regulator (lots of voltage, since these are basically fool-proof) and whatever was attached to that. Not saying all SMPS's are unstable, but it's not as easy as a linear supply. The SMPS feedback loop is not inherently stable. Computer power supplies are even more fun, since these can make a decent welder (tens of amps continuous, even more peak).