Q. I'm not convinced that totalizing machines can't be used for a Condorcet method, through a device similar to the one used to implement range on noncomputerized totalizing machines. You simply implement all the pairwise elections...
A. Yes, except for two problems.
First, 30-candidate elections would not be doable. Because, a voter would have to specify his opinion on all 30×29/2=435 candidate pairs. That is too much to ask. 30 inputs is reasonable to ask, especially if a lot are allowed to be left blank or filled with some common value, as in range voting. But 435 is too much.
(The Congo held a presidential election in July-August 2006 with 33 candidates.)
Second, the machine would have to reject "invalid" votes in which the input corresponded to a cyclic directed graph, i.e. was crazy and clearly not intended by the voter since logically meaningless. Totalizing machines cannot do that detection and rejection.
(Third, I don't think most human voters would like providing this kind of input anyhow – they'd find it confusing and annoying. )
For IRV voting, it is even worse since IRV is not additive at all, even in terms of pairwise results, and also since IRV votes are rank orderings and detecting whether a vote is a rank ordering, and rejecting it as "invalid" otherwise, is beyond noncomputerized totalizing machines.
So: no. Borda, Condorcet and IRV voting (the latter for even more reasons) cannot be done on these machines, but range (including both averaging- and totalling-based range voting) can be done.