George Bernard Shaw crystallised longstanding biases when he declared that Handel's operas were “only stage concerts for shewing off the technical skill of the singers”. David Alden, a longstanding maverick director and hero of Regie-philes, made his reputation in part through his striking interpretations of Handel. If anything, his production of Alcina, which he first staged at the Opéra National de Bordeaux in 2012 (with many of the same singers), pushes too far in the opposite direction to the theatrically static fossil of Shaw's stereotype.

But Alden's spirit of invention produced many engaging results that enhanced the musical wizardry on opening night in the high New Mexican desert. For its part, the anonymous libretto Handel set was a kind of fantasia on its source (episodes from Ariosto's epic poem Orlando furioso). In his version – realised with the vivid phantasmagoria of Gideon Davey's set and costumes, Malcolm Rippeth's lighting, and Beate Vollack's choreography – Alden relocates the sorceress Alcina's enchanted isle to an abandoned theatre.

The young knight Ruggiero has sought refuge here from the humdrum of his routine life, conjuring Alcina as his ideal woman: “opera diva, entertainer, seductress,” notes the director. He had in mind the scenario of Woody Allen's 1985 film The Purple Rose of Cairo, whose protagonist (Mia Farrow) loses herself at the movies, watching the same one repeatedly until its characters break the fourth wall and step off the screen into her drab world.

Alongside the opera's chief love triangle, in which Alcina and Ruggiero's disguised fiancée Bradamante both vie for Ruggiero, Alden thus underscores the conflict between the constraints of reality and the liberating imagination (which gave an added poignancy to Ruggiero's “Verdi prati” in Act 2, his bittersweet ode to the magic world to which he must bid adieu). The situation of Act 1's abandoned theatre developed to reveal an increasingly convoluted sequence of images and allusions as the opera progressed. Oronte, Alcina's general, appeared to be an usher at the theatre and, at the same time, one of her victims – she has a penchant for transforming men into beasts.

Alcina's threats to subject Bradamante to this treatment were accompanied by a busy visual scenario suggesting a sinister natural history museum. In the third act, the perplexity continued to multiply as a parade of ironic references to 1950s suburban life became prominent. A large skeletal spine dangling at the front of the stage, like an inverted question mark or hook, never disclosed its purpose. It became an emblem of the eccentric, unanswered questions that loomed throughout the production. Another image Alden fetishised is a bright magenta glove Alcina wields as her magic wand. 

Yet the visuals were theatrically engaging and thought-provoking, their unpredictability a dramaturgical embodiment of the ornamentation in the da capo repeats in arias. As to the charge that Alden's constant theatrical counterpoint distracts from Handel's music, I became aware that there was in fact a nuanced spectrum of stagings. Some were over-the-top numbers drawing from vaudeville, a kind of valentine to show business, but others were entrancingly minimal and focused on the 'affect', enhanced by a highly poetic use of shadow and lighting contrasts. 

As an elegant Alcina driven to drink, Elza van den Heever sang with stirring beauty – the devotion with which she conveyed her love for Ruggierio in act one would not have been out of place as a Passion aria – but also commanded thrilling power (and an unnervingly diabolical cackle). Her sister Morgana, at first ready to abandon her lover Oronte in favor of the disguised Bradamante, became an especially fascinating character in Anna Christy's vivid and virtuosic performance.

Paula Murrihy's Ruggiero captured the emotional complexity Alden clearly intended, decoding the young man's conflicting emotional loyalties. With her virtuosic confidence as Bradamante (thrilling in her revenge aria), Daniela Mack occasionally brought to mind a young Cecilia Bartoli. Tenor Alek Shrader's Oronte benefited from a terrific comic presence, sometimes distorting his voice for dramatic effect, but capable of genuinely sweet lyricism when reunited with Morgana. Alden conceived the subplot role of the adolescent Oberto (poignantly sung by Jacqueline Stucker) as a kind of proto-Cherubino attracted to Alcina while searching for his father (one of her victims). Christian Van Horn brought a large voice to his aria as Melisso. 

Harry Bicket showed again why he is so reliable with this music, conducting a performance replete with subtle pleasures, from unexpected touches of texture (he used a Baroque harp as a continuo instrument to complement himself on harpsichord and the singers) to dramatically revelatory dynamic contrasts. His intuition of the right pacing to bring out Alden's staging was unfailingly persuasive.  

Alcina's spell turns out to be the spell that opera, art in general, casts as long as we submit.