I'm assessing the case to get a Brompton Dock in town, which would work out at £2.50/day at the regular user rate. If Bromptons come to Edinburgh like this, a big detail will be corporate sign-ups (ie employer offers free membership with subsidised or free hire rates to reduce demand for parking spaces or similar measures). Contact me direct if you think we can develop interest/sign ups, as there may be a way to deliver this.
Options I've used (when doing work which involved going out to Loanhead) were mix & match. Train to HYM and then cut across via Meadows to Newington Road. If I saw a bus heading for Penicuik/Loanhead I'd race to next stop and get on board (7 to Captains Road also an option as it got me up the hill. If no bus by Liberton Brae, not worth bothering. Likewise going back - Ride down main road to bypass and if a bus spotted - use it, if no bus by summit - keep riding.
Modern Bromptons are pretty tough, as I've not broken main frame or rear triangle in at least 5 years now. Did shear off a steerer in a crash in 2010 but it was an old steerer from 1989 frame, and may have been damaged in previous crashes. For personal use do change the saddle as the current design does not agree with the 'bearing surfaces' of many riders for regular use, and do consider a tougher bottom bracket. I trash a FAG unit in 12-18 months. Steerer bearings are also a weak point (going slack) for forceful riders.