You can connect to build VM with RDP and debug those tests. If this is just a VM size issue, we can enable 4-core VMs with 7Gb of memory for you. Note that they are twice more expensive than a standard ones. We can provide 1-week free trial.
You can use any cloud you prefer and select a VM of specific size there. We charge much less for builds on own cloud - $10/month per job.
Setup is easy and we for sure will assist.
Hard part is maintaining your own VHD. If you are OK with it, then you should try. If not - we are now working on providing pre-baked lightweight VHD in specific regions on each major cloud. If you are interested, we can arrange a testing of this VHD for you (currently on Azure, but will be created for GCE and AWS too very soon). It is not the same VHD we use in production -- new one we share is much more lightweight with only essential stuff.