By the way, the phenomenon of having most of the calendar falling on the same days of the week for subsequent years occurs when between the two years in question MarCheshvan and Kislev have 30 days each, and there is an extra Adar. That results in a span of 385 days between the dates, which is exactly 55 weeks. The other possibilities of # of days (353, 354, 355, 383, 384) are not divisible by 7 (so are not complete weeks).
The above only applies to the part of the calendar that is a constant number of days (between 1 Adar or Adar Sheni and 29 MarCheshvan).
Until this discussion, I never knew that Asara bTevet could be on Friday two days in a row. I think the only way is if in the first year, Rosh Hashana is on Shabbos in a leap year with 383 days, and the second year Rosh Hashana is on Thursday in a regular year of 355 days.
More generally, I never considered how it might work out to have two years in a row for the non-constant parts of the year(Kislev, and Tevet + Shvat). As somewhat of a calendar enthusiast (not an expert!) I might try working that out myself (though I am sure that the experts already have that at their fingertips).