The Harvard site usually does not aspirate the consonants but occasionally the speaker makes a soft aspiration, a few of the professors don’t sound very enthusiastic about reading though.
I know it sounds weird but the Gloucester girl school seems to have an RP accent in some recordings. They make mistakes a few times but they get it unaspirated most of the time
It is difficult for native English speakers to pronounce ‘t’ ‘c’ and ‘p’ without aspirating them. Because, under most circumstances, these consontants are always aspirated in English, and because the lack of aspiration in these consonants is usually associated with voicing them (i.e. using the voicebox: t becomes d, c becomes g, p becomes b), we very often pronounce them as if they were the English equivalents of these letters. Because we also have alternate pronunciations of the aspirated consonants (ph=f, etc) with which we can differentiate them in our pronunciations, and because perfect pronunciation of a dead language is impossible anyway, most English speakers don’t worry about it a lot.
I get the feeling that unvoiced is continually being associated with aspiration in most languages nowadays, possibly under influence of English or just sheer laziness.