KHSO4 is usually supplied as a mixture of KHSO4.xK2SO4 (x<1) crystals that are hydrites and have absorbed a little SO3 in their mass.
But I am afraid that with KHSO4, you will form the non-soluble potassium alum.
Phosphoric acid will also form the insoluble AlPO4.
Alternatively, you could try saturated ammonium chloride solution that might form among others, a mixture of hexaminealuminium chloride and basic aluminium chlorides that all are water soluble.
[Al(NH3)6]Cl3 and AlCl3 + Al(OH)Cl2 + Al(OH)2Cl + Al(OH)3
But firstly, try this with a small amount, in order to see if it works.
1). Reaction study of aluminium chloride with ammonia and mechanisms leading to aluminium nitride, Journal of the European Ceramic Society, 16(5), 521-527, (1996) https://www.sciencedirect.com/science/article/abs/pii/0955221995001689
2). Water-soluble basic aluminum compounds, United States Patent 2196016, (1940)