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I'm trying to understand why an increase of Ca2+ entering into the cell, increases the force of the heart contractions. Based on what I have watched in many lectures videos on Youtube (this one- "interactive biology" for example on 4:45), Ca2+ basically slows the repolarization in phase II of the action-potential membrane, and I don't understand how it does the cardiac cells more contractible. Or maybe the answer is pinned in the words "typical cardiomyocytes" and then I didn't get it.
The answer is a bit more complex. Calcium ions have a lot of effects in the cardiac myocyte. Apart from the increased contractility (positive inotropy), extracellular calcium concentration also alters chronicity as you mention by altering the rate of repolarisation. An attempt at a simplified picture of the inotropic effects follows:
First is to increase the contractility via directly sensitizing the tropomyosin system. Have a look here. Quoting the paper, "...In both cardiac and skeletal muscle, the force-generating molecular motors (crossbridges) are turned on by increasing the intracellular free calcium level that regulates the troponin-tropomyosin system. However, calcium activation is a two-way process in the sense that activated crossbridges also affect the troponin-tropomyosin system...An increase in Ca2+ activity causes an azimuthal shift of tropomyosin around the filament (by about 30 degrees), thereby increasing the probability of low-force crossbridge interaction, a process which by cooperative effects induces further tropomyosin movement (by an additional 10 degrees) which results in the open state of the filament characterized by forceful cross-bridge interaction...". Hence, higher the intracellular concentration of Calcium, greater is the maximum force.
Sarcomere length also affects the sensitivity to calcium. This increase in contractility is not because of calcium but is mediated by calcium. The reason has something to do with lateral filament lattice spacing decreasing, increasing the probability of cross-bridge formation, increased strain on titin alters lattice spacing and myosin packing. 
As I said, this is a bit too oversimplified. There a lot of inter-regulations taking place. Have a look at these papers here.
Two different but related processes i.e excitation- contraction coupling could possibly answer your question. Please see the simple diagram: https://image.slidesharecdn.com/heartcirculation-120511091224-phpapp01/95/heart-circulation-47-728.jpg?cb=1336727680 "Ca2+ basically slows the repolarization in phase II of the action-potential membrane" what you said is one of the excitation phase during which Ca2+ influx cause more Ca2+ release from endoplasmic reticulum, increasing Ca2+ concentration in the cytoplasm leading to more binding of Ca2+ to troponin C and subsequently increase force of contraction.
