Your GSM carrier might have different APNs for 3G and 4G service. If so, you might be able to find a way to use Tasker to automate the modification of your data APN between the two. I've looked, but all I can find is using Tasker + APNDroid to append "apndroid" to the APN name to disable mobile data entirely. Useful in its own way, but not in your use-case. If anyone else can figure out a way to make it happen though, I think the potential is there.
Otherwise, I found a forum post describing how to use Tasker to toggle 4G data. They list instructions for toggling LTE; I don't know if it will work for toggling HSDPA/HSPA+ 4G on your Note II but it might be worth a shot. Here are the juicy bits, modified slightly for clarity:
You must be rooted and running a custom ROM that supports 4G toggling (i.e. AOKP).
- Step 1: Download Secure Settings
- Step 2: Open the app, go to Options and scroll down to Custom ROM Actions and ensure that "LTE" is checked
- Step 3: Open up Tasker and create a profile entitled "4G On" and choose your first context (App = Chrome)
- Step 4: Click New Task at the top of the tasks list and name it 4G On.
- Step 5: Click the + button and scroll to Plugins and you will see Secure Settings. Click it.
- Step 6: You will see edit configuration; click edit
- Step 7: Now you will see a list of the options you have enabled in Secure Settings. We care about 4G, so scroll down to LTE and click it. Then it will ask you what state you want LTE to be in. This is the 4G On profile, so click On. Save and apply the task.
- Step 8: Repeat steps 3-7, but now choose the context you want for 4G to be off, name your profile and task 4G Off, and when you get to the configuration settings in Secure Settings, make sure you check Off for the state of LTE. Save and apply the task.