You might want to try this:
1) Download DAEMON tools.
http://www.daemon-tools.cc
2) Make ISO images (or another format supported by DAEMON tools) of your game CD's with the program of your choice.
3) Mount the image of the install CD with DAEMON tools.
4) Mount the virtual CD-ROM/DVD-ROM drive created by DT as a CD-ROM in DOSBox.
5) Install and run the game in DOSBox.
Videos seem to get a bit more stuttery, but I'm not really sure if just a case of my computer running out of steam. DOSBox image mounting seems to do a better job, but this has worked for me in the past when I have needed disc swapping.
When a game wants you to change the CD, just jump out of DOSBox (release the mouse if it's locked + maybe get out of full screen mode), right-click on the DT icon in your taskbar, browse to the mounted image, select 'eject tray' (dunno if that really necessary), mount the needed CD's image, return to DOSBox and away you go (I hope)!