POMC

POMC seems like a good candidate for height increase with knockout increasing height and overexpression decreasing height.

The melanocortin system in articular chondrocytes: melanocortin receptors, pro-opiomelanocortin, precursor proteases, and a regulatory effect of alpha-melanocyte-stimulating hormone on proinflammatory cytokines and extracellular matrix components.

"The pro-opiomelanocortin (POMC)-derived neuropeptide alpha-melanocyte-stimulating hormone (alpha-MSH) mediates its effects via melanocortin (MC) receptors. This study was carried out to investigate the expression patterns of the MC system and the effects of alpha-MSH in human articular chondrocytes.
Articular chondrocytes established from human osteoarthritic joint cartilage were analyzed by reverse transcription-polymerase chain reaction (RT-PCR) and Western blotting for the expression of MC receptors, POMC, and prohormone convertases (PCs). MC-1 receptor (MC-1R) expression in articular cartilage was further studied by immunohistochemistry. Ca(2+) and cAMP assays were used to monitor alpha-MSH signaling, while studies of alpha-MSH function were performed in cultures with chondrocyte micromass pellets stimulated with alpha-MSH. Expression of cytokines and extracellular matrix (ECM) components was determined by real-time RT-PCR, Western immunoblotting, and enzyme-linked immunosorbent assays.
MC-1R expression was detected in articular chondrocytes in vitro and in articular cartilage in situ. In addition, expression of transcripts for MC-2R, MC-5R, POMC, and PCs was detected in articular chondrocytes. Stimulation with alpha-MSH increased the levels of intracellular cAMP, but not Ca(2+), in chondrocytes. Both messenger RNA and protein expression of various proinflammatory cytokines, collagens, matrix metalloproteinases (MMPs), and SOX9 was modulated by alpha-MSH{So POMC can influence height by modulation all these genes}.
Human articular chondrocytes are target cells for alpha-MSH. The effects of alpha-MSH on expression of cytokines and MMPs suggest that this neuropeptide plays a role in inflammatory and degenerative processes in cartilage. It is conceivable that inflammatory reactions can be mitigated by the induction of endogenous MCs or administration of alpha-MSH to the affected joints. The induction pattern of regulatory and structural ECM components such as collagens as well as SOX9 and anabolic and catabolic cytokines points to a function of alpha-MSH as a trophic factor in skeletal development during endochondral ossification rather than as a factor in homeostasis of permanent cartilage."

"After 48 hours of stimulation with 10−6M α-MSH, the levels of mRNA for COL1A1, COL2A1, and, in particular, COL10A1 were profoundly elevated "<-It would seem like this would be good for height increase if POMC increasing a-MSH was regulating the height altering effects.

"Treatment with α-MSH significantly stimulated gene expression of MMPs 2, 7, and 9, while gene expression of MMP-13 displayed only a nonsignificant tendency for up-regulation."  Sox9, TGFB1, and IL6 also increased in expression.

"Processing of POMC by these PCs yields the MCs adrenocorticotropin (ACTH) and α-, β-, and γ-MSH, as well as the endogenous opioid β-endorphin (β-ED)."

"Since MC-2R selectively binds ACTH, human articular chondrocytes may respond to not only α-MSH but also ACTH."<-So a-MSH may compete with ACTH.  So ACTH may be better than a-MSH for height gain which is why POMC could decrease height by competing with the more pro-height ACTH.  If something other than POMC can upregulate ACTH.

" α-MSH might be a positive inducer of growth of the long bone, which has been described in earlier studies utilizing γ2-MSH. Administration of γ2-MSH elevates growth plate height in general, and augments the proliferating and hypertrophic zone in particular. ACTH induces expression of type II and type X collagens in bone marrow–derived stem cells and in costal chondrocytes, which are representative of committed resting chondrocytes in the growth plate. Presumably, ACTH promotes the development of the OA chondrocyte phenotype of progenitor cells and increases matrix production and differentiation of early committed chondrocytes"