Hello Japamor,
Well first of all giving your current host I think is the best thing to do, setting up Cronjobs is not really much of a big deal for a decent systems Administrator.
Dependant upon the host though if you are on a self-managed server then you should also have the access to set them up and it is not a bad thing to learn as they can be very common. Another option might be to seek the assistance of a remote administrator to assist you, this would allow you to maintain your current host, while accomplishing the required task.
Finally if you do choose to move I would certainly like the opportunity to earn your hosting. At
http://www.Caro.Net we can help you with your migration and setting up Cronjobs for our clients is something we can certainly assist you with, in addition to offering you various control panels.
Thanks in advance, good luck, and Happy Holidays.