I don't see anything questionable about those verbs, Dishanta is a
simple past tense because the psalmist had already been anointed.
Veshavti should be read literally, "and + past tense", and denotes a
highly assured prediction, which is practically done. Note that major
commandments are often formulated as weqatal.
I recall reading a book on English rhetoric which showed on
Shakespeare's many quotes the mixture of tenses in poetry, which it
said was a common rhetoric device with some obscure name that I won't
recall easily.
Vadim Cherny
Bryant J. Williams III wrote:
For instance, in Ps. 23, all the finite verbs are PC1 except for v. 5,
‏dishanta. (The questionable form veshavti in v. 6 I leave out).
[b-hebrew] Narrative vs Poetry,
Vadim Cherny, 02/10/2010