You wouldn't use National Rail anyway as that just directs you to the relevant train company. National Rail themselves do not sell rail tickets.
I can not see where $322 comes from. The Anytime Single standard class is £132.20 and Off Peak Day Single is £125.10. If we use a £1= US$1.25 that £132.20 is US$165.25 so even $188 on R2R/Omio feels high.
I have just looked on National Rail and those are the fares I am seeing there, so not sure where you see $322.
Anytime 1st class is £211.50= US$264.35.
Those are the most expensive fares for the route.
But if you split the fares (and avoid Advance Fares for now)-
Anytime Day Single MiM to London Paddington is £46.80
Off Peak Day Single (all trains except, on weekdays before 0930 and 1700-1900) London Kings Cross to Attleborough £54.40. Total £100.20, saving £32.
Then pay your own tube fare across London
But that £54.40 London KC to Attleborough can be further reduced by taking the small time penalty of travelling from Liverpool Street to Cambridge and splitting the fares.
Cambridge to Attleborough is £21.80 Off Peak Day Single and London Liverpool Street to Cambridge is £25.10 Off Peak Day Single (any time after 0930 on weekdays). But also, even in the evening Peak Advance Fares of £21.40 are usually available until 1 minute before departure. At 1638 tonight an advance fare is still there on the 1726 and 1731 trains LLS-Cambridge- peak of the evening peak fares.
Do split advance fares for a few weeks time MiM to Paddington, London Liv Street to Cambridge and Cambridge to Attleborough and it should come to £28 + £8 + £21.80= £58 + your tube fare.
All those prices can be further reduced by 34% using your TwoTogether Railcard.
Personally I always use Northern Rail, which always has the best fares. That website works fine for people in North America.