Solving Leeper (1991) model
You have the government's flow budget constraint (re-written in real terms):

$b_{t} + m_{t} + \tau_{t} = g + \frac{m_{t-1}}{\pi_{t}} + R_{t-1}\frac{b_{t-1}}{\pi_{t}}$ (1)

Now all you need to do is substitute (2) and the policy rules (also, I don't think Leeper's utility function had a $\delta$ but that's not important) and linearise. I.e linearise:

$b_{t} +δc[\frac{R_{t}}{R_{t}-1}] + (\gamma_{0} + \gamma_{1}b_{t-1} + \psi_{t}) = g +\frac{δc[\frac{R_{t-1}}{R_{t-1}-1}]}{\pi_{t}} + (\alpha_{0} + \alpha_{1} \pi_{t-1} + \beta \theta_{t-1}) \frac{b_{t-1}}{\pi_{t}}$ (2)

Note: I left some $R_{t}$ and $R_{t-1}$ in there but you will have to substitute the monetary policy rule there as well. Then all you do is a Taylor approximation around the deterministic steady state. Just a warning, the algebra will be very hairy, it took me several tries to get it right.

OP requested some more reading on this topic so I'll add a list here:

[1] Loyo (1999), Tight Money Paradox on the Loose: A Fiscalist Hyperinflation

[2] Woodford (1998), Public Debt and the Price Level

[3] Woodford (2000), Fiscal Requirements for Price Stability

[4] Leeper &amp; Leith (2016), Understanding Inflation as a Joint
Monetary-Fiscal Phenomenon

I have many more but start with these.