If you 'touch' a continent, even in transit you are deemed to have entered it.

As Asia is your continent of origin, you can only re-enter it once. If you wanted to go through to LHR, then NA then back to Asia, you cannot within the rules as your transit on the way to LHR would have been your re-entry to Asia.

If you need to originate in Asia, the 'SWP-Europe Transfer without stopever in Asia' clause cannot apply.

Also, you cannot re-enter your originating continent until you have traversed both the Pacific and Atlantic oceans.

So the following may be valid as you are not originating in asia:
jfk-bkk-syd-lhr-jfk