How hard do I need to cycle to simulate the effort of this hill climb?

Interesting question. For climbing upwards the hill you must raise your potential energy against gravitational field to $mgh$. IMO, it not depends on hill steepness. You can ride very slowly with lowest gear up the steep hill and do the same job with legs as riding low hill, but just with highest gear and at your maximum speed. So other things being equal the job you have made increasing potential energy in gravity field must be equals to job in straight road over-coming rolling friction and drag force for distance $D$. Expressing in formula would be :

$$ (F_{rr}+F_{d})cdot D = mgh + Delta W_o $$

Where $F_{rr}$ is rolling resistance force acting over distance $D$ and $F_d$ is a drag force acting over same distance. $h$ is hill height and $Delta W$ is negative work done when you climb up the hill by same road rolling resistance & air drag forces.

Assumptions :

• We will consider steep hill, so that $mgh gg Delta W_o $, and this additional work can be safely ignored
• Because you mentioned indoors training air drag force can be safely ignored, i.e. assumed to be zero

Using these assumptions, and expressing for rolling resistance force, gives :

$$ C_{rr}~mgcdot D = mgh $$

Solving for $D$ gives :

$$ D = frac {h}{C_{rr}} $$

Thus for knowing needed for riding indoors cycling distance $D$ for getting the same effect as when running up the hill - you just need to know hill height $h$ and rolling resistance coefficient $C_{rr}$. Finding hill height is not a problem at all. But finding rolling resistance indoors can be a challenge. Because it hingly depends on bicycle technology, wheel materials, resisting method, and finally about which gear you will use for cycling. As I've understood you will use a stationary training bicycle, thus due to gear used - it will induce to you a different rolling resistance coefficient. Anyway, I'm sure you can detect this rolling resistance coefficient by other empirical means.

For simple cases rolling resistance coefficient can be expressed as :

$$ C_{rr}={sqrt {z/d}} $$

where $z$ is the sinkage depth and $d$ is the diameter of the rigid wheel.