Ask Mr. Smarty Plants

Unfortunately, I couldn't find any information on the use of plant growth regulators (PGR) on Sorghastrum nutans (Indiangrass) — 3 to 8 ft, Andropogon gerardii (big bluestem) — 4 to 8 ft,  Schizachyrium scoparium (little bluestem) — 2 to 4 ft, or Andropogon virginicus (broomsedge bluestem) — 2 to 5 feet. Most of the research has been done on turf grasses (e.g., bentgrass and bermuda grass).  I did, however, find one study on taller grasses, the cereal grasses:

Triticum aestivum (wheat) — 1.5 m (4.9 ft)

Avena sativa (oats) — 0.9m (3 ft)

Hordeum vulgare (barley) — 1m (3.3 ft)

A. Rajala and P. Peltonen-Sainio ["Plant Growth Regulator Effects on Spring Cereal Root and Shoot Growth",  Agronomy Journal 93:946-943 (2001)] reported that the application of two plant growth regulators (PGR), chlormequat chloride (CCC) and trinexapac-ethyl, reduced the shoot length by as much as 20% and increased the number of tillers (shoots) per plant, but did not increase the total mass of the plants. They did not, however, use the PGRs in conjunction with mowing or burning.  If you are interested, you might be able to find this journal with the article at a nearby univesrity (e.g., Washington University in St. Louis). With only the information from this article, I would think that application of GDRs to your taller species would likely reduce their height some, but I would guess not very much.

You might consider using other shorter grasses or sedges—or ones with more attractive foliage and/or seedheads, although I happen to think the ones you mentioned are attractive.  Here are some suggestions for native grasses and seges found in eastern Missouri:

Bouteloua dactyloides (buffalograss) is a turf grass, but it would be ideal for sunny prairie areas since its maximum height is only 12 inches.  The USDA Plants Database shows it occurring in a few counties in Missouri, one of which is St. Louis County just south of your county, St. Charles County.

Carex blanda (eastern woodland sedge) is an evergreen sedge that grows in sun, part shade and shade, to less than 2 ft.  You can see more information from Illinois Wildflowers.

Carex pensylvanica (Pennsylvania sedge) another low-growing sedge (<1.5 ft), with more information from Illinois Wildflowers.

Chasmanthium latifolium (Inland sea oats) is a bunch grass that can grow as high as 4 ft, but it does this very happily in shade and part shade.  It also has very attractive seed heads that are often used in flower arrangements.

Elymus canadensis (Canada wildrye) is another 2 to 4 ft bunch grass with an attractive seed head often used in floral arrangements.  It will do well in sun, part shade and shade.

Koeleria macrantha (prairie Junegrass) is a low-growing clump grass (<1.5 ft) that is often used in prairie restoration projects.  Here is more information from Illinois Wildflowers.

Muhlenbergia capillaris (hairawn muhly) is an attractive bunch grass that generally grows to less than 2 ft.  Here is more information from Missouri Botanical Gardens.

Sporobolus heterolepis (prairie dropseed) is another attractive bunch grass that generally grows to around 2 ft, with more information from Missouri Botanical Gardens.

Bouteloua dactyloides

Carex blanda

Carex pensylvanica

Chasmanthium latifolium

Elymus canadensis

Koeleria macrantha

Muhlenbergia capillaris

Sporobolus heterolepis