How to extract water from a solution in formamide
I'd like to determine the water content in a sample without buying an expensive machine (like [a] Karl Fischer titrator).


Rather than try to extract the water and measure it volumetrically, I think you could try to measure its activity, or else perform your own Karl-Fischer titration, which does not necessarily require any equipment.

Water activity measurement

Practically this means hygrometers.  That may sounds like another expensive machine, but E-bay tells me that capacitive hygrometers are available for under $20.  If your sample consists of sucrose, glucose, and glycerol, those substances are unlikely to interfere with capacitive hygrometry measurements of water activity.

You might even get very crude accuracy by incubating a mirror at a known (chilled) temperature, and then waving it above your water/sucrose/glucose/glycerol sample, seeing if dew forms, and then repeating the process at several different temperatures.

Karl Fischer titration on your own

As an alternative, couldn't you just set up your own Karl Fischer titration?  Commercial titrators often use coulometric detection for better accuracy, but setting up a volumetric titration is pretty easy.  You need:


Methanol (or some other alcohol)
Imidazole (or some other amine base)
Sulfur dioxide
Iodine


Imidazole and sulfur dioxide should be combined in a 1:1 molar ratio in an excess of methanol.  Iodine should be dissolved in methanol.

A 2012 paper has a nice description of how to do KF with visual end-point determination.  You just need to buy a KF titration solution, or make your own:


  Commercially available [...] Test Kit from [...] was used for reference moisture determination. All the equipments needed were provided with the kit. It consisted of two-component ethanol-based reagents: [a] working medium containing [a mixture of] imidazole, sulphur dioxide and diethanolamine, and [separately a titrant solution] containing iodine. According to manufacturer's instructions for use, 20 mL of [working medium] was added to the titration vessel, which was then tightly sealed with a septum. The titrant was delivered through the septum with a syringe to react with the present water, until a color change from colorless to yellow occurred. A known amount of sample was added by a syringe to the titration vessel via septum, and a newly filled titration syringe was used for a new titration until the color change from colorless to yellow occurred. Consumption volume of the titrant was read off the titration syringe. The water content, in percent by volume, was calculated from the consumption of the titrant and the sample volume.


If you've diluted with formamide


  I've dissolved a sample (approx. 20 g; composed of sucrose, glycerol and glucose syrup, water) in 50 ml formamide and like now to separate the water fraction again. 


The nice part about both water activity measurement and Karl Fischer titration is that they are both sensitive and accurate enough to still work on your sample even after dilution or dissolution in formamide.