Crystallization of zinc sulfate monohydrate
TL; DR: obtaining a reasonably big single crystal of $\ce{ZnSO4 * H2O}$ seems to be a tricky task, whereas one can easily obtain $\ce{ZnSO4 * H2O}$ as a result of thermal dehydration of heptahydtare above $\pu{70 ^\circ C}$ in a form of melt, and above $\pu{120 ^\circ C}$ – as a polycrystalline solid material.



I finally got across to suitable references to back up my comments. In nature zinc sulfate monohydrate occurs as mineral gunningite, always in a form of efflorescence deposition on the surface of sphalerite and other minerals and doesn't form single crystals [1]:


  Surface and ground waters carrying dissolved oxygen attack
  the sphalerite, yielding soluble sulphates of zinc [...]:
  
  $$\ce{ZnS + 2 O2 -&gt; ZnSO4}$$
  
  [...] In the presence of abundant water all of the soluble salts are removed. If, however, the conditions are such that the supply of water is restricted or evaporation takes place, the metal-bearing solutions become supersaturated with the consequent precipitation of a number of hydrates of zinc, manganese, and iron of which gunningite, $\ce{ZnSO4 * H2O}$, is one.


Thermal dehydration among zinc sulfate hydrates has been studied with DTA in several publications. The most relevant and thorough investigation [2, p. 471] suggests the following scheme:

$$\ce{ZnSO4 * 7 H2O (s) -&gt;[\pu{37 ^\circ C}] ZnSO4 * 6 H2O (s) -&gt;[\pu{70 ^\circ C}] ZnSO4 * H2O (l) -&gt;[\pu{120 ^\circ C}] ZnSO4 * H2O (s) -&gt;[\pu{285 ^\circ C}] ZnSO4 (s)}$$

Original text in German:


  Festgestellt werden vier endotherme Effekte: bei etwa $\pu{37 ^\circ C}$ verwandelt sich das Heptahydrat in Hexahydrat; bei etwa $\pu{70 ^\circ C}$ geht das Hexahydrat in Monohydrat über, wobei teilweise Schmelzen im Kristallwasser auftritt. Bei etwa $\pu{120 ^\circ C}$ siedet die Schmelze, Wasser scheidet 
  sich ab, bis das feste Monohydrat zurückbleibt; bei etwa $\pu{285 ^\circ C}$ erfolgt der Übergang des Monohydrates in wasserfreies Salz. 


The tricky part is that monohydrate can be isolated in crystal form, but it initially isolates as a melt, and only above $\pu{120 ^\circ C}$ makes a polycrystalline solid phase (occurs as white powder or granules).

Aqueous solubility $\omega_2$ for zinc sulfate $\ce{ZnSO4}$ in mass% of a solute ($\omega_2 = m_2/(m_1 + m_2)$, where $m_2$ is the mass of solute and $m_1$ the mass of water) as a function of temperature ($T$) from CRC Handbook [3, p. 5-172]:

\begin{array}{r|rrrrrrrr}
T,\,\pu{^\circ C} &amp; 0 &amp; 10 &amp; 20 &amp; 25 &amp; 30 &amp; 40 &amp; 50 &amp; 60 &amp; 70 &amp; 80 &amp; 90 &amp; 100 \\
\hline
\omega_2,~\% &amp; 29.1 &amp; 32.0 &amp; 35.0 &amp; 36.6 &amp; 38.2 &amp; 41.3 &amp; 43.0 &amp; 42.1 &amp; 41.0 &amp; 39.9 &amp; 38.8 &amp; 37.6
\end{array}

With this in mind, what can be suggested is to prepare a saturated at $\pu{70 ^\circ C}$ solution, and then slowly increase the temperature (e.g. using a thermostat), hoping that zinc sulfate monohydrate starts to crystallize (using the decrease in solubility starting from $\pu{60 ^\circ C}$). 

According to [4, entry 3575, p. 470], solubility of $\ce{ZnSO4 * H2O}$ also decreases in this interval: $\pu{101 g}/\pu{100 g}~\ce{H2O}$ at $\pu{70 ^\circ C}$, and $\pu{87 g}/\pu{100 g}~\ce{H2O}$ at $\pu{105 ^\circ C}$. The difference is rather small, so I wouldn't expect rapidly-grown large crystals.

References


Jambor, J. L.; Boyle, R. W. The Canadian Mineralogist 1962, 7 (2), 209–218.  
Balarew, C.; Trendafelov, D.; Gerganova, M. Monatshefte für Chemie 1971, 102 (2), 465–473. DOI 10.1007/BF00909340 (in German).  
Haynes, W. M.; Lide, D. R.; Bruno, T. J. CRC handbook of chemistry and physics: a ready-reference book of chemical and physical data.; 2017; Vol. 97.  
Perry, D. L. Handbook of inorganic compounds, 2nd ed.; Taylor &amp; Francis: Boca Raton, 2011. ISBN 978-1-4398-1461-1.