Actually, with IB not having any up-front or "ticket" charges, it will have no effect on commissions since all IB commission charges are on a per contract basis. I always close one calendar at a time and never try to close two calendars with the same trade. I wouldn't recommend legging out of one calendar as that really makes your trade directional after one of the legs has been closed.
As for not being able to use TWS from work. I was in the same boat due to corporate IP settings and firewalls - but got around the issue by creating an Amazon web server and then RDP-ing into it and running TWS from there (I RDP using a tablet, but your work PC can also be used if you are able to). If you go down this road, don't use the free "micro sized" AWS server as that will be too slow for TWS. I used a medium sized windows server, and only bring it up when I'm trading or preparing to do so, and the cost is typically around $20 a month. Compared to using brokers other than IB, I'll more than make up for that extra $20 with a couple of trades per month so its a good solution for me.