Welcome BT,
All sorts of tips in the stickies and threads in this forum, and sure enough you'll find the best way for you. I was a no-hoper for anything other than Blue, but with a little pre-planning and a couple of tweaks to routings I'm able to get the 600tps from this year.
First you want to be clear what you want out of Silver (eg. Lounge access) and ask if you're prepared to pay a little towards that. For example, a long-weekend somewhere close in Europe (fly CE) can get you 80tps and lift you over the 600 point line.

With 6 x trips to Sth Am in cheapo economy, you have 12 sectors at 30tps, so 360tps in the 'probable' bag and 240tps to find. It sounds like you do one WT+ rtn holiday a year (150tps), so add the 80 CE and you're only 10 short! That's one extra sector in Sth Am on Lan along the line.
As others have said paid upgrades on the WT legs can work for you too (have to say I'd hate those sectors in WT for work), or get work to pay for more flexible H,B,Y tickets which may well be cost effective anyhow in your line of work as the return leg may be easier to revise.

The one thing to watch is tying all the trips in with your BAEC year, which'll end on 8th of some month.
Good luck.