Great questions! Let's tackle them one at a time.
For your first question regarding: diuretic dosing at various CKD stages
You are correct that increasing the dose of diuretic, either by increasing the drip rate or by increasing the amount of IV pushes, would not be a universally successful therapy. The greater the degree of kidney disease, the less likely the tubules (in particular, the ascending loop of Henle) will respond to a loop diuretic. Of course, many outpatients with CKD stage 4 and CHF are placed on combination of loop diuretic + thiazide diuretic with some natriuretic effect. The difference between the outpatient CKD-4/CHF patient and the inpatient CKD-4/CHF patient would have to be the presence of AKI in the latter patient. This AKI is likely a result of an alteration in the "renal perfusion pressure" (RPP). More on that below.
Regarding your second question: when to initiate CRRT?
This becomes a little complicated, depending on whether you are asking a cardiologist or nephrologist. First, let's try to find common ground between both groups. Both nephrologists and cardiologists would agree that, in acute decompensated CHF patients, there is an accumulation of salt and water because of a decrease in RPP (among other factors as well; but for this discussion, let's focus on the RPP exclusively). The RPP is simply the difference in renal artery pressure and renal vein pressure (or, more accurately, afferent arteriole pressure - efferent arteriole pressure. The lower the RPP, the less intraglomerular pressure exists to filter sodium and water. Thus, high RPP's lead to greater filtration.
Now, the differences.
Nephrologists believe that the RPP is low because of decreased perfusion to the kidneys by the weakened heart. The afferent arteriolar pressure has decreased. To increase RPP, therefore, one should increase afferent arteriolar pressure. This can be accomplished by increasing cardiac output (difficult to do) or increasing volume (easier to do). Most nephrologists would rec'd cautious fluid administration, and if not possible because of severe symptomatic pulmonary edema, gentle natriuresis. All of these therapies would be aimed at lowering the RPP.
Now, if you ask a cardiologist, they'd probably take the view that you've articulated in your question. Simply place the patient on ULTRAFILTRATION (not CRRT because the latter would be perform solute removal, which is not indicated for treatment of pulmonary edema). UF would allow for a "controlled" or "predictable" amount of fluid to be removed. An increasing number of heart-failure specialists are purchasing UF-only machines for this purpose. However, keep in mind the many complications of placing a patient on an artificial ultrafiltration machine. The biggest would be worsening the already existing AKI. It has been my experience that non-nephrologists who use extracorporeal therapies (like UF-only machines) induce AKI, making it even harder to re-establish fluid homeostasis.
In the end, the best course of action would be to have an intellectual discussion with intelligent and team-oriented nephrologists and cardiologists.
If you'd like more information, click here for a great presentation on the Cardiorenal syndrome, which is what you've described in your question.