Such opportunities do not come in Mozart and Beethoven.
"As a bass instrument, I tend to follow the harmonic lines of the piece," Reese explains. "But I do enjoy this big harmonic contribution that I make."
As for solos, Reese reminds me of a 2007 NZSO concert, where composer John Psathas put him in the spotlight with the spectacular Planet Damnation. At the time we were told he had "given up the last nine months of his life to mastering the precise business of just how to bash the hell out of this virtuoso music".
"All the planets must have aligned to create a composer with such a great idiomatic feel for my instrument," he says. "Planet Damnation is the most difficult piece I have ever played. It's not hard for the sake of being hard, but it really pushed the boundaries in terms of what the timpani are capable of."
Post-Psathas, nothing has been the same. "I view everything I play now through the lens of John's work," says Reese. "John's challenges are as relevant in Beethoven's music as they are in his own."
The contemporary offerings on the NZSO Soloists programme are fairly unthreatening specimens; a newly commissioned Portrait from New Zealander Kenneth Young, Arvo Part's minimalist classic Fratres and Rain Tree by Toru Takemitsu.
Reese explains how the 1981 percussion trio is one of a series of Takemitsu works inspired by the theme of water.
He outlines its source in the writing of the Japanese poet Oe, who describes the exotic plant with capacious leaves that retain moisture for later "showers".
On stage, Takemitsu's world will be captured by Lenny Sakovsky, Bruce McKinnon and Jeremy Fitzsimons, but Reese also has an important role, off-stage.
"Takemitsu indicates very specific lighting in the score, with the lights beneath the players, creating a striking effect through the instruments themselves. It's like rays of light on to the tree." He will be in charge of operating these lights - "a task so challenging that it's usually done by another percussionist".
Reese is clearly thrilled to be involved with a chamber music presentation in the big performance space of Auckland's Town Hall, which he says is the NZSO's favourite New Zealand venue.